tag:blogger.com,1999:blog-48764763224313624312024-02-20T11:09:06.822-08:00Solutions - Optics - Eugene Hecht - 5th Edition Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-4876476322431362431.post-78606358342585050022020-07-03T13:50:00.003-07:002020-07-03T13:50:23.057-07:00Chapter #13 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. After a while, a cube of rough steel (10 cm on a side) reaches
equilibrium inside a furnace al a temperature of 400°C. Knowing that its
total emissivity is 0.97, determine the rate at which the cube radiates
energy from each face. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2.
A somewhat typical person has a total naked area of about 1.4 m2 and an
average skin temperature of 33°C„Determine the net power radiated per
unit area, the irradiance or more precisely the exitance, if the
person's total emissivity is 97% and the environment is room temperature
(20°C). How much energy does that body radiate per second? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3.
Suppose that we measure the emitted exitance from a small hole in a
furnace to be 22.8 W/cm2, using an optical pyrometer of some sort.
Comptite the internal temperature of the furnace. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4.
The temperature of an object resembling a blackbody is raised from 200 K
to 2000 K. By how much does the amount of energy it radiates increase? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5.
Your average skin temperature is about 33°C. Assuming you radiate as
does a blackbody at that temperature, at what wavelength do you emit the
most energy? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6.
What is the wavelength that carries away the most energy when an object
resembling a blackbody radiates energy into a room-temperature (20°C)
environment? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7.
The surface temperature of a class O blue-white star is around 40 × 103
K. At what frequency will it radiate most of its energy? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8.
When the Sun's spectrum is photographed, using rockets to range above
the Earth's atmosphere, it is found to have a peak in its spectral
exitanee at roughly 465 nm. Compute the Sun's surface temperature,
assuming it to be a blackbody. This approximation yields a value that is
about 400 K too high. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9.
An object resembling a blackbody emits a maximum amount of energy per
unit wavelength in the red end of the visible spectrum p (λ = 680 nm).
What's its surface temperature? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10.
The energy per unit area per unit time per wavelength interval emitted
by a blackbody at a temperature T' is given by...At a specific
temperature, the total power radiated per unit area of the blackbody is
equal to the area under the corresponding Iλ versus A curve. Use this to
derive the Stefan-Boltzmann Law. [Hint: To clean up the exponential,
change variables in the integral so that...Use the fact that ...where
the gamma function is given by ... and the Riemann zeta function for n =
3 is ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12.
In the atomic domain, energy is often measured in electron-volts.
Arrive at the following expression for the energy of a light quantum in
eV when the wavelength is in nanometers:...What is the energy of a
quantum of 600-nm light? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13.
Figure P.13.12 shows the spectral irradiance impinging on a horizontal
surface, for a clear day, at sea level, with the Sun at the zenith. What
is the most energetic photon we can expect to encounter (in eV and in
J)?Figure P.13.12... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14.
Suppose we have a 100-W yellow lightbulb (550 nm) 100 m away from a
3-cm diameter shuttered aperture. Assuming the bulb to have a 2.5%
conversion to radiant power, how many photons will pass through the
aperture if the shutter is opened for ... s? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15.
The solar constant is the radiant flux density at a spherical surface
centered on the Sun having a radius equal to that of the Earth's mean
orbital radius; it has a value of 0.133-0.14 W/cm2. If we assume an
average wavelength of about 700 nm, how many photons at most will arrive
on each square meter per second of a solar cell panel just above the
atmosphere? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16.
A 50.0-cm3 chamber is filled with argon gas to a pressure of 20.3 Pa at
a temperature of 0°C. All but a negligible number of these atoms are
initially in their ground states. A flash tube surrounding the sample
energizes 1.0% of the atoms into the same excited state having a mean
life of 1.4 X 10-8as. What is the maximum rate at which photons are
subsequently emitted by the gas, of course it falls off with time?
Assume both that spontaneous emission is the only mechanism at work and
that the medium is an ideal gas. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17.
Show that for a system of atoms and photons in equilibrium at a
temperature T the ratio of the transition "rates of stimulated to
spontaneous emission is given by... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18.
A system of atoms in thermal equilibrium is emitting and absorbing
2.0-eV light photons. Determine the ratio of the transition rates of
stimulated emission to spontaneous emission at a temperature of 300 K.
Discuss the implications of your answer. [Hint. See the previous
problem.] <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19. Redo the previous problem for a temperature of 30.0 × 103K and compare the results of both calculations. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22.
For a system of atoms (in equilibrium) having two energy levels, show
that at high temperatures where kBT >> ...-...,-, the number
densities of the two states tend to become equal. [Hint. Form the ratio
of die transition rates for total emission to absorption.] <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23.
Radiation at 21 cm pours down on the Earth from outer space. Its origin
is great clouds of hydrogen gas. Taking the background temperature of
space to be 3.0 K, determine the ratio of the transition rates of
stimulated emission to spontaneous emission and discuss the result. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27.
The beam (λ = 632.8 nm) from a He-Ne laser, which is initially 3.0 mm
in diameter, shines on a perpendicular wall 100 m away. Given that the
system is diffraction limited, how large is the circle of light on the
wall? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28.
Make a rough estimate of the amount of energy that can be delivered by a
ruby laser whose crystal is 5.0 mm in diameter and 0.050 m long. Assume
the pulse of light lasts 5.0 X 10-6 s. The density of aluminum oxide
(A12O3) is 3.7 × 103 kg/m3. Use the data in the discussion of Fig. 13.6
and the fact that the chromium ions make a 1.79 eV lasing transition.
How much power is available per pulse? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29.
What is the transition rate for the neon atoms in a He-Ne laser if the
energy drop for the 632.8 nm emission is 1.96 eV and the power output is
1.0 mW? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31. Given that a ruby laser operating at 694.3 nm has a frequency bandwidth of 50 MHz, what is the corresponding linewidth? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32. Determine the frequency difference between adjacent axial resonant cavity modes for a typical gas laser 25 cm long (n ≈ 1). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />35.
A He-Ne c-w laser has a Doppler-broadened transition. bandwidth of
about 1.4 GHz at 632.8 nm. Assuming n - 1.0, determine the maximum
cavity length for single-axial mode operation. Make a sketch of the
transition linewidth and the corresponding cavity modes. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.35p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />36. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.36p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />37.
Show (hat the maximum electric-field intensity, Emax, that exists for a
given irradiance l is...where n is the refractive index of the medium. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.37p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />38.
A He-Ne laser operating at 632.8 nm has an internal beam-waist diameter
of 0.60 mm. Calculate the full-angular width, or divergence, of the
beam. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.38p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />39.
What would the pattern look like for a laserbeam diffracted by the
three crossed gratings of Fig. P. 13.29?Figure P.13.29... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.39p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />40.
Make a rough sketch of the Fraunhofer diffraction pattern that would
arise if a transparency of Fig. P. 13.30a served as the object. How
would you filter it to get Fig. P. 13.30b?Figure P.13.30(a) ...(b) ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.40p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />41. Repeat the previous problem using Fig. P.13.31 instead.Figure P.13.31 (Photos courtesy R. A. Phillips.)(a) ...(b) ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.41p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />42. Repeat the previous problem using Fig. P.13.32 this time.Figure P.13.32 (Photos courtesy R. A. Phillips.)(a) ...(b) ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.42p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />43.
Returning to Fig. 13.32, what kind of spatial filter would produce each
of the patterns shown in Fig. P.l 3.33?Figure P.13.33 (Photos courtesy
D. Dutton, M. P. Givens, and R. E. Hopkins)(a) ...(b) ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.43p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />44.
With Fig. 13.31 in mind, show that the transverse magnification of the
system is given by -fi/fi and draw the appropriate ray diagram. Draw a
ray up through the center of the first lens at an angle 6 with the axis.
From the point where that ray intersects Σt draw a ray downward that
passes through the center of the second lens at an angle .... Prove
that.... Using the notion of spatial frequency, from Eq. (11.64), show
that k1 at the object plane is related to k, at the image plane
by...What docs this mean with respect to the size of the image which fi
> f1? What can then be said about the spatial periods of the input
data as compared with the image output? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.44p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />45.
A diffraction grating having a mere 50 grooves per cm is the object in
the optical computer shown in Fig. 13.31. If it is coherently
illuminated by plane waves of green light (543.5 nm) from a He-Ne laser
and each lens has a 100,cm focal length, what will be the spacing of the
diffraction spots on the' transform plane? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.45p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />46.
Imagine that you have a cosine grating (i.e., a transparency whose
amplitude transmission profile is cosinusoidal) with a spatial period of
0.01mm. The grating is illuminated by quasimonochromatic plane waves of
A = 500 nm, and the setup is the same as that of Fig. 13.31, where the
focal lengths of the transform and imaging lenses are 2.0 m and 1.0 m,
respectively.a) Discuss the resulting pattern and design a filler that
will pass only the first-order terms. Describe it in detail.b) What will
the image look like on 2/ with that filter in place?c) How might you
pass only the dc term, and what would the image look like then? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.46p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />47.
Suppose we insert a mask in the transform plane of the previous
problem, which obscures everything but the m = +1 diffraction
contribution. What will the reformed image look like on Σi? Explain your
reasoning. Now suppose we remove only the m = +1 or the in m = -1 term.
What will the re-formed image look like? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.47p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />48.
Reterring to the previous two problems with the cosine gratying
oriented horizontally, make a sketch of the electric-field amplitude
along y' with no filtering. Plot the corresponding image irradiance
distribution. What will the electric field of the image look like if the
dc term is filtered out? Plot it. Now plot the new irradiance
distribution. What can you say about the spatial frequency of the image
with and without the filter in place? Relate your answers to Fig. 11.13.
<a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.48p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />49.
Replace the cosine grating in the previous problem with a "square" bar
grating, that is, a series of many fine alternating opaque and
transparent bands of equal width. We now filter out all terms in the
transform plane but the zeroth and the two first-order diffraction
spots. These we determine to have relative irradianccs of 1.00, 0.36,
and 0.36: compare them with Figs. 7.32a and 7.33. Derive an expression
for the general shape of the irradiance distribution on the image
plane—make a sketch of it. What will the resulting fringe system look
like? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.49p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />50.
A fine square wire mesh with 50 wires per cm is placed vertically in
the object plane of the optical computer of Fig. 13.30. If the lenses
each have 1,00-m focal lengths, what must be the illuminating
wavelength, if the diffraction spots on the transform plane are to have a
horizontal and vertical separation of 2.0 mm? What will be the mesh
spacing as it appears on the image plane? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.50p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />51.
Imagine that we have an opaque mask into which arc punched an ordered
array of circular holes, all of the same size, located as if at the
corners of the boxes of a checkerboard. Now suppose our robot puncher
goes mad and makes an additional batch of holes essentially randomly all
across the mask. If this screen is now made the object in Problem
13.39, what will the diffraction pattern looklike? Given that the
ordered holes are separated from their nearest neighbors on the object
by 0.1 mm, what will be the spatial frequency of the corresponding dots
in the image? Describe a filter that will remove the random holes from
the final image. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.51p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />52.
Imagine that we have a large photographic transparency on which there
is a picture of a student made up of a regular array of small circular
dots, all of the same size, but each with its own density, so that it
passes a spot of light with a particular field amplitude. Considering
the transparency to be illuminated by a plane wave, discuss the idea of
representing the electric-field amplitude just beyond it as the product
(on average) of a regular two-dimensional array of top-hat functions
(Fig. 11.4, p. 523) and the continuous two-dimensional picture function:
the former like a dull bed of nails, the latter an ordinary photograph.
Applying the frequency convolution theorem,, what does the distribution
of light look like on the transform plane? How might it be filtered to
produce a continuous output image? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.52p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />53.
The arrangement shown in Fig. P. 13.43 is used to convert a collimated
laserbeam into a spherical wave. The pinhole cleans up the beam; that
is, it eliminates diffraction effects due to dust and the like on the
lens. How does it manage it?Figure P.13.43 (a) and (b) A high-power
laserbeam before and after spatial filtering. (Photos courtesy Lawrence
Livermore National Laboratory.)(a) ...(b) ...(c) ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.53p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />54.
What would happen to the speckle pattern if a laserbeam were projected
onto a suspension such as milk rather than onto a smooth wall? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=13.54p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-26298991490962045442020-07-03T13:50:00.001-07:002020-07-03T13:50:09.842-07:00Chapter #12 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8.
Suppose we set up a fringe pattern using a Michelson Interferometer
with a mercury vapor lamp as the source. Switch on the lamp in your
mind's eye and discuss what will happen to the fringes as the mercury
vapor pressure builds to its steady-slate value. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9.
We wish to examine the irradiance produced on the plane of observation
in Young's Experiment when the slits are illuminated simultaneously by
two monochromatic plane waves of somewhat different frequency, E1, and
E2, Sketch these against time, taking A! = 0.8A2. Now draw the product
E1 E2 (at a point P) against time.What can you say about its average
over a relatively long interval? What does (E1 + E2)2 look like? Compare
it with Ef + E\. Over a time that is long compared with the periods of
the waves, approximate ((E1 + E2)2)T <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10.
With the previous problem in mind, now consider things spread across
space at a given moment in time. Each wave separately would result in an
irradiance distribution I1 and I2. Plot both on the same space axis and
then draw their sum I1 + I2. Discuss the meaning of your results.
Compare your work with Fig. 7.16. What happens to the net irradiance as
more waves of different frequency are added in? Explain in terms of the
coherence length. Hypothetically, what would happen to the pattern as
the frequency bandwidth approached infinity? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11.
With the previous problem in mind, return to the autocorrelation of a
sine function, shown in Fig. 11.37. Now suppose we have a signal
composed of a great many sinusoidal components. Imagine that you take
the autocorrelation of this complicated signal and plot the result (use
three or four components to start with), as in part (e) of Fig. 11.37.
What will the autocorrelation function look like when the number of
waves is very large and the signal resembles random noise? What is the
significance of the T - 0 value? How does this compare with the previous
problem? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12.
Imagine that we have the arrangement depicted in Fig. 12.3. If the
separation between fringes (max. to max.) is 1 mm and if the projected
width of the source slit on the screen is 0.5 mm, compute the
visibility. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13.
Referring to the slit source and pinhole screen arrangement of Fig. P.
12.6, show by integration over the source that...Figure P.12.6... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14. Carry out the details leading to the expression for the visibility given by Eq. (12.22). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15.
Under what circumstances will the irradiance on ∑a in Fig. P.12.8 be
equal to 4I0, where I0 is the irradiance due to either incoherent point
source alone?Figure P.12.8... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16.
Suppose we set up Young's Experiment with a small circular hole of
diameter 0.1 mm in front of a sodium lamp ... as the source. If the
distance from the source to the slits is 1 m, how far apart will the
slits be when the fringe pattern disappears? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18. Show that Eqs. (12.34) and (12.35) follow from Eqs. (12.32) and (12.33), <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19.
Return to Eq. (12.21) and separate it into two terms representing a
coherent and an incoherent contribution, the first arising from the
superposition of two coherent waves with irradiances of ... and ...
having relative phase of α12(T), and the second from the superposition
of incoherent waves of irradiance ... and .... Now derive expressions
for Icoh/Iincoh and for Iincoh/Itotal, Discuss the physical significance
of this alternative formulation and how we might view the visibility of
fringes in terms of it. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20.
Imagine that we have Young's Experiment, where one of the two pinholes
is now covered by a neutral-density filter that cuts the irradiance by a
factor of 10, and the other hole is covered by a transparent sheet of
glass, so there is no relative phase shift introduced. Compute the
visibility in the hypothetical case of completely coherent illumination.
<a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21.
Suppose that Young's double-slit apparatus is illuminated by sunlight
with a mean wavelength of 550 nm. Determine the separation of the slits
that would cause the fringes to vanish. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24.
We wish to construct a double-pinhole setup illuminated by a uniform,
quasimonuchromalic, incoherent slit source of mean wavelength 500 nm and
width b, a distance of 1.5 m from the aperture screen. If the pinholes
are 0.50 mm apart, how wide can the source be if the visibility of the
fringes on the plane of observation is not to be less than 85%? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25.
Suppose that we have an incoherent, quasimonochromatic, uniform slit
source, such as a discharge lamp with a mask and fitter in front of it.
We wish to illuminate a region on an aperture screen 10.0 m away, such
that the modulus of the complex degree of coherence everywhere within a
region 1.0 mm wide is equal to or greater than 90% when the wavelength
is 500 nm. How wide can the slit be? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26.
Figure P. 12.17 shows two incoherent quasimonochromatic point sources
illuminating two pinholes in a mask. Show that the fringes formed on the
plane of observation have minimum visibility when...where m = ±1, ±3,
±5....Figure P.12.17... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27.
Imagine that we have a wide quasimonochromatic source (λ - 500 nm)
consisting of a series of vertical, incoherent, infinites-imally narrow
line sources, each separated by 500 μm. This is used to illuminate a
pair of exceedingly narrow vertical slits in an aperture screen 2.0 m
away. How far apart should the apertures be to create a fringe system of
maximum visibility <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=12.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-65928729983190475942020-07-03T13:49:00.007-07:002020-07-03T13:49:57.691-07:00Chapter #11 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. Determine the Fourier transform of the function...Make a sketch of ...{E(x)}. Discuss its relationship to Fig. 11.11. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2. Determine the Fourier transform of...Make a sketch of it. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3. Determine the Fourier transform of...Make a sketch of F(to), then sketch its limiting form as T -> ±∞. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4. Show that = ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5. Determine the Fourier transform of the function f(x) = A cosk0x. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9. Given that ...{f(x)} = F(k) and ...{h(x}} = H(k) if a and b are constants, determine ...{af(x) + bh(x) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10.
Figure P.l 1.7 shows two periodic functions, f(x) and h(x), which are
to be added to produce g(x). Sketch g(x); then draw diagrams of the real
and imaginary frequency spectra, as well as the amplitude spectra for
each of the three functions.Figure P.11.7... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11.
Compute the Fourier transform of the triangular pulse shown in ' Fig.
P. 11.8. Make a sketch of your answer, labeling all the pertinent values
on the curve.Figure P.11.8... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12.
Given that ...{f(x)} = F(k), introduce a constant scaling factor 1/a
and determine the Fourier transform of/f(x/a). Show that the transform
of f(-x) is F(-k). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13.
Show that the Fourier transform of the transform, ...{f(x)}, equals
2пf(-x), and that this is not the inverse transform of the transform,
which equals f(x). This problem was suggested by Mr. D. Chapman while a
student at the University of Ottawa. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14.
The rectangular function is often defined as...where it is set equal to
½ at the discontinuities (Fig. P.11.11). Determine the Fourier
transform of...Notice that this is just a rectangular pulse, like that
in Fig. 11.16, shifted a distance x0 from the origin.Figure P.11.11... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15.
With the last two problems in mind, show that ...{(l/2п)sinc (½x)} -
rect(k). starting with the knowledge that ...{rect(x)} - sinc(½k),in
other words, Eq.(7.58) with L = a, where a = 1. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16. Utilizing Eq. (11.38), show that ...-l{...{f(x)}} = f(x). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17. Given ...{f(x)}, show that ...{f(x - x0)} differs from it only by a linear phase factor. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18. Prove that f...h = h .../directly. Now do it using the convolution theorem. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21.
Suppose we have two functions, f(x, y) and h(x, y), where both have a
value of 1 over a square region in the xy-plane and are zero everywhere
else (Fig. P.11.16). If g(X, Y) is their convolution, make a plot of
g(X, 0).Figure P.11.16... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22.
Referring to the previous problem, justify the fact that the
convolution is zero for ... when h is viewed as a spread function. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23. Use the method illustrated in Fig. 11.23 to convolve the two functions depicted in Fig. P.11.18.Figure P.11.18... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24. Given that ... show that after shifting one of the functions an amount x0, we get ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27.
Prove analytically that the convolution of any function f(x) with a
delta function, δ(x), generates the original function f(X). You might
make use of the fact that δ(x) is even. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28.
Prove that δ(x - x0) ... f(x) =f(X - x0) and discuss the meaning of
this result. Make a sketch of two appropriate functions and convolve
them. Be sure to use an asymmetrical f(x). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29. Show that ...{f(x) cos k0x} = [F(k - k0) + F(k + k0)]/2 and that ...{f(x) sin k0x] = [F(k-k0) - F(k + k0)]/2i. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30. Figure P.11.23 shows two functions. Convolve them graphically and draw a plot of the result. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32. Given the function...determine its Fourier transform. (See Problem 11.11.) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33. Given the function f(x) = δ(x + 3) + δ (x - 2) + δ (x-5), convolve it with the arbitrary function h(x).Figure P.11.23... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34.
Make a sketch of" the function arising from the convolution of the two
functions depicted in Fig. P.l 1.26.Figure P.l 1.26... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />35.
Figure P. 11.27 depicts a rect function (as defined above) and a
periodic comb function. Convolve the two to get g(x). Now sketch the
transform of each of these functions against spatial frequency k/2π =
1/λ. Check your results with the convolution theorem. Label all the
relevant points on the horizontal axes in terms of d—like the zeros of
the transform of f(x).Figure P.11.27... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.35p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />36.
Figure P.l 1.28 shows, in one dimension, the electric field across an
illuminated aperture consisting of several opaque bars forming a
grating. Considering it to be created by taking the product of a
periodic rectangular wave h(x) and a unit rectangular function f(x),
sketch the resulting electric field in the Fraunhofer region.... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.36p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />37.
Show (for normally incident plane waves) that if an aperture has a
center of symmetry (i.e., if the aperture function is even), then the
diffracted field in the Fraunhofer case also possesses a center of 1
symmetry. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.37p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />38.
Suppose a given aperture produces a Fraunhofer field pattern E(Y, Z).
Show that if the aperture's dimensions are altered such that the
aperture function goes from ... (y, z) to ... (αy, βz), the newly
diffracted field will be given by... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.38p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />39.
Show that when f(t) - A sin (ωt + ε), Cff(T) - (A2/2) cos ωt, which
confirms the loss of phase information in the autocorrelation. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.39p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />40.
Suppose we have a single slit along the y-direction of width b where
the aperture function is constant across it at a value of ... What is
the diffracted field if we now apodize the slit with a cosine function
amplitude mask? In other words, we cause the aperture function to go
from ... at the center to 0 at ±b/2 via a cosinusoidal dropoff. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.40p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />41. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.41p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />42. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.42p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />43. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.43p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />44. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.44p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />45. Show, from the integral definitions, that ....... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.45p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />46. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.46p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />47. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.47p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />48. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.48p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />49.
Figure P . l 1.34 shows a transparent ring on an otherwise opaque mask.
Make a rough sketch of its autocorrelation function, taking l to be the
center-to-center separation against which you plot that function.Figure
P.11.34... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.49p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />50.
Consider the function in Fig. 11.35 as a cosine carrier multiplied by
an exponential envelope. Use the frequency convolution theorem to
evaluate its Fourier transform. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=11.50p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-60494576125961237682020-07-03T13:49:00.005-07:002020-07-03T13:49:44.608-07:00Chapter #10 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. A point source S is a perpendicular distance R away from the
center of a circular hole of radius a in an opaque screen. If the
distance to the periphery is (R + ℓ), show that Fraunhofer diffraction
will occur on a very distant screen whenλR» a2/2What is the smallest
satisfactory value of R if the hole has a radius of 1 mm, ℓ≤λ/10, and λ -
500 nm? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3.
Referring back to the multiple antenna system on p.451, compute the
angular separation between successive lobes or principal maxima and the
width of the central maximum. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4.
Examine the setup of Fig. 10.3 in order to determine what is happening
in the image space of the lenses; in other words, locate the exit pupil
and relate it to the diffraction process. Show that the configurations
in Fig. P. 10.5 are equivalent to those of Fig. 10.3 and will therefore
result in Fraunhofer diffraction. Design at least one more such
arrangement.Figure P.10.5... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6.
The angular distance between the center and the first minimum of a
single-slit Fraunhofer diffraction pattern is called the half-angular
breadth; write an expression for it. Find the corresponding half-linear
width (a) when no focusing lens is present and the slit-viewing screen
distance is L, and (b) when a lens of focal length f2 is very close to
the aperture, Notice that the half-linear width is also the distance
between the successive minima. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7.
A single slit in an opaque screen 0.10 mm wide is illuminated (in air)
by plane waves from a krypton ion laser (λ0 — 461.9 nm). If the
observing screen is 1.0 m away, determine whether or not the resulting
diffraction pattern will be of the far-field variety and then compute
the angular width of the central maximum. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8.
A narrow single slit (in air) in an opaque screen is illuminated by
infrared from a He-Ne laser at 1152.2 nm, and it is found that the
center of the tenth dark band in the Fraunhofer pattern lies at an angle
of 6.2° off the central axis. Please detennine the width of the slit.
At what angle will the tenth minimum appear if the entire arrangement is
immersed in water (nw, = 1.33) rather than air (na = 1.00029)? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9.
A collimated beam of microwaves impinges on a metal screen that
contains a long horizontal slit that is 20 cm wide. A detector moving
parallel to the screen in the far-field region locates the first minimum
of irradiance at an angle of 36.87° above the central axis. Determine
the wavelength of the radiation. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14.
Show that for a double-slit Fraunhofer pattern, if a = mb, the number
of bright fringes (or parts thereof) within the central diffraction
maximum will be equal to 2m. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15.
Two long slits 0.10 mm wide, separated by 0.20 mm, in an opaque screen
are illuminated by light with a wavelength of 500 nm. If the plane of
observation is 2.5 m away, will the pattern correspond to Fraunhofer or
Fresnel diffraction? How many Young's fringes will be seen within the
central bright band? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17.
What is the relative irradiance of the subsidiary maxima in a
three-slit Fraunhofer diffraction pattern? Draw a graph of the
irradiance distribution, when a = 2b, for two and then three slits. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22.
Starting with the irradiance expression for a finite slit, shrink, the
slit down to a minuscule area element and show that it emits equally in
all directions. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25.
Show that Fraunhofer diffraction patterns have a center of symmetry
[i.e., I(Y, Z) = I( -Y, -Z)], regardless of the configuration of the
aperture, as long as there are no phase variations in the field over the
region of the hole. Begin with Eq. (10.41). We'll see later (Chapter
11) that this restriction is equivalent to saying that the aperture
function is real. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26.
With the results of Problem 10.14 in mind, discuss the symmetries that
would be evident in the Fraunhofer diffraction pattern of an aperture
that is itself symmetrical about a line (assuming normally incident
quasimonochromatic plane waves). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27.
From symmetry considerations, create a rough sketch of the Fraunhofer
diffraction patterns of an equilateral triangular aperture and an
aperture in the form of a plus sign. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28.
Figure P. 10.17 is the irradiance distribution in the far field for a
configuration of elongated rectangular apertures. Describe the
arrangement of holes that would give rise to such a pattern and give
your reasoning in detail.Figure P.10.17 (Photo courtesy R. G. Wilson,
Illinois Wesleyan University.)... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29.
In Fig. P.10.18a and b arc the electric field and irradiance
distributions, respectively, in the far field for a configuration of
elongated rectangular apertures. Describe the arrangement of holes that
would give rise to such patterns and discuss your reasoning.Figure
P.10.18 (Photo courtesy R. G. Wilson, Illinois Wesleyan University.)... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30.
Figure P. 10.19 is a computer-generated Fraunhofer irradiance
distribution. Describe the aperture that would give rise to such a
pattern and give your reasoning in detail.Figure P.10.19 (Photo courtesy
R. G. Wilson, Illinois Wesleyan University.)... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31.
Figure P. 10.20 is the electric-field distribution in the far field for
a hole of some sort in an opaque screen. Describe the aperture that
would give rise to such a pattern and give your reasoning in
detail.Figure P.10.20 (Photo courtesy R. G. Wilson, Illinois Wesleyan
University.)... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32.
In light of the five previous questions, identify Fig. P.10.21,
explaining what it is and what aperture gave rise to it.Figure P.10.21
(Photo courtesy R. G. Wilson, Illinois Wesleyan University.)... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />35. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.35p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />36.
Verify that the peak irradiance I1 of the first "ring" in the Airy
pattern for far-field diffraction at a circular aperture is such that
I1/I(0) = 0.0175. You might want to use the fact that... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.36p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />38.
No lens can focus light down to a perfect point because there will
always be some diffraction. Estimate the size of the minimum spot of
light that can be expected al the focus of a lens. Discuss the
relationship among the focal length, the lens diameter, and the spot
size. Take the f-number of the lens to be roughly 0.8 or 0.9, which is
just about what you can expect for a fast lens. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.38p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />39.
Figure P. 10.24 shows several aperture configurations. Roughly sketch
the Fraunhofer patterns for each. Note that the circular regions should
generate Airy-like ring systems centered at the origin.Figure P.10.24...
<a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.39p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />40.
Suppose that we have a laser emitting a diffraction-limited beam (λ0 =
632.84 nm) with a 2-mm diameter. How big a light spot would be produced
on the surface of the Moon a distance of 376 × 103 Ion away from such a
device? Neglect any effects of the Earth's atmosphere. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.40p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />41.
If you peered through a 0.75-mm hole at an eye chart, you would
probably notice a decrease in visual acuity. Compute the angular limit
of resolution, assuming that it's determined only by diffraction; take
λ0 = 550 nm. Compare your results with the value of 1.7 × 10-4 rad,
which corresponds to a 4.0-mm pupil. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.41p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />42. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.42p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />43. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.43p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />44. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.44p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />45.
The neoimpressionist painter Georges Seurat was a member of the
pointilhst school. His paintings consist of an enormous number of
closely spaced small dots (...) of pure pigment. The illusion of color
mixing is produced only in the eye of the observer. How far from such a
painting should one stand in order to achieve the desired blending of
color? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.45p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />46.
The Mount Palomar telescope has an objective mirror with a 508-em
diameter. Determine its angular' limit of resolution at a wavelength of
550 nm, in radians, degrees, and seconds of arc. How far apart must two
objects be on the surface of the Moon if they are to be resolvable by
the Palomar telescope? The Earth-Moon distance is 3.844 × 3 08 m; take
λ0 = 550 nm. How far apart must two objects be on the Moon if they are
to be distinguished by the eye? Assume a pupil diameter of 4.00 mm. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.46p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />47. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.47p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />48. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.48p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />49. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.49p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />50. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.50p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />51.
A transmission grating whose lines are separated by 3.0 × 10-6 m is
illuininated by a narrow beam of red light (λ0 = 694.3 nm) from a ruby
laser. Spots of diffracted light, on both sides of the undefeated beam,
appear on a screen 2.0 m away. How far from the central axis is each of
the two nearest spots? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.51p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />52.
A diffraction grating with slits 0.60 × 103 cm apart is illuminated by
light with a wavelength of 500 nm. At what angle will the third-order
maximum appear? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.52p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />53.
A diffraction grating produces a second-order spectrum of yellow light
(λ0 = 550 nm) at 25°. Determine the spacing between the lines on the
grating. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.53p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />54. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.54p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />55.
White light falls normally on a transmission grating that contains 1000
lines per centimeter. At what angle will red light (λ0 = 650 nm) emerge
in the first-order spectrum? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.55p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />56.
Light from a laboratory sodium lamp has two strong yellow (components
at 589.5923 nm and 588.9953 nm. How far apart in the first-order
spectrum will these two lines be on a screen 1.00 m from a grating
having 10 000 lines per centimeter? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.56p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />57. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.57p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />58. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.58p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />59.
Sunlight impinges on a transmission grating that is formed with 5000
lines per centimeter. Does the third-order spectrum overlap the
second-order spectrum? Take red to be 780 nm and violet to be 390 nm. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.59p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />60. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.60p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />61.
Light having a frequency of 4.0 × 1014 Hz is incident on a grating
formed with 10 000 lines per centimeter. What is the highest-order
spectrum that can be seen with this device? Explain. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.61p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />62.
Suppose that a grating spectrometer while in vacuum on Earth sends
500-nm light off at an angle of 20.0° in the first-order spectrum. By
comparison, after landing on the planet Mongo, the same light is
diffracted through 18.0°. Determine the index of refraction of the
Mongoian atmosphere. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.62p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />63.
Prove that the equationa(sin θm - sin θ1) = mλ [10.61]when applied to a
transmission grating, is independent of the refractive index. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.63p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />64. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.64p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />65.
A high-resolution grating 260 nun wide, with 300 lines per millimeter,
at about 75° in autocollimation has a resolving power of just about 106
for λ = 500 nm. Find its free spectral range. How do these values of R
and (∆λ)fsr compare with those of a Fabry-Perot etalon having a 1-cm air
gap and a finesse of 25? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.65p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />66.
What is the total number of lines a grating must have in order just to
separate the sodium doublet (λ1 = 5895.9 Å, λ2 = 5890.0 A) in the third
order? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.66p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />67.
Imagine an opaque screen containing 30 randomly located circular holes.
The light source is such that every aperture is coherently illuminated
by its own plane wave. Each wave in turn is completely incoherent with
respect to all the others. Describe the resulting far-field diffraction
pattern. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.67p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />68.
Imagine that you are looking through a piece of square woven cloth at a
point source (λ0 = 600 nm) 20m away. If you see a square arrangement of
bright spots located about the point source (Fig. P. 10.41), each
separated by an apparent nearest-neighbor distance of 12 cm, how close
together are the strands of cloth?Figure P.10.41 (Photo by E. H.)... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.68p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />69. Perform the necessary mathematical operations needed to arrive at Eq. (10.76). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.69p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />70.
Referring to Fig. 10.38, integrate the expression dS = 2πρ2 sin (φ dφ
over the lth zone to get the area of that zone,...Show that the mean
distance to the lth zone is...so that the ratio Al/rl is constant <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.70p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />71. 'Derive Eq. (10.84). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.71p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />72. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.72p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />73.
Collimated light from a krypton ion laser at 568.19 nm impinges
normally on a circular aperture. When viewed axially from a distance of
1.00 m, the hole uncovers the first half-period Fresnel zone. Determine
its diameter <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.73p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />74.
Plane waves impinge perpendicularly on a screen with a small circular
hole in it. It is found that when viewed from some axial point P the
hole uncovers P of the first half-period zone. What is the irradiance at
P in terms of the irradiance there when the screen is removed? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.74p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />75. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.75p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />76. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.76p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />77. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.77p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />78. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.78p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />79. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.79p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />80. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.80p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />81. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.81p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />82. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.82p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />83.
A collimated beam from a ruby laser (694.3 nm) having an irradiance of
10 W/m2 is incident perpendicularly on an opaque screen containing a
square hole 5.0 mm on a side. Compute the irradiance at a point on the
central axis 250 cm from the aperture. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.83p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />84. Use the Comu spiral to make a rough sketch of ... (w1+w2)/2 for ∆w = 5.5. Compare your results with those of Fig. 10.57. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.84p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />85.
The Fresnel integrals have the asymptotic forms (corresponding to large
values of w) given by......Using this fact, show that the irradiance in
the shadow of a semi-infinite opaque screen decreases in proportion to
the inverse square of the distance to the edge, as z1 and therefore v1
become large. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.85p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />86. What would you expect to see on the plane of observation if the half-plane 2 in Fig. 10.58 were semi-transparent? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.86p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />87.
Plane waves from a collimated He-Ne laserbeam (λ0 = 632.8 nm) impinge
on a steel rod with a 2.5-mm diameter. Draw a rough graphic
representation of the diffraction pattern that would be seen on a screen
3.16 m from the rod. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.87p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />88.
Make a rough sketch of the irradiance function for a Fresnel
diffraction pattern arising from a double slit. What would the Cornu
spiral picture look like at point P0? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.88p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />89.
Make a rough sketch of a possible Fresnel diffraction pattern arising
from each of the indicated apertures (Fig. P. 10.50).Figure P.10.50... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.89p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />90. Suppose the slit in Fig. 10.54 is made very wide. What will the Fresnel diffraction pattern look like? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.90p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />91.
A long narrow slit 0.10 mm wide is illuminated by light of wavelength
500 nm coming from a point source 0.90 m away. Determine me irradiance
at a point 2.0 m beyond the screen when the slit is centered on, and
perpendicular to, the line from the source to the point of observation.
Write your answer in terms of the unobstructed irradiance. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.91p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />92. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.92p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />93. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=10.93p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-76475236752137293922020-07-03T13:49:00.003-07:002020-07-03T13:49:31.204-07:00Chapter #9 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. Returning to Section 9.1, let...And ...where the wavefront shapes
are not explicitly specified, and ... and ... are complex vectors
depending on space and initial phase angle. Show that the interference
term is then given by...You will have to evaluate terms of the
form...for T>> T (take another look at Problem 3.10). Show that
Eq. (9.109) leads to Eq. (9.11) for plane waves. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2.
In Section 9.1 we considered the spatial distribution of energy for two
point sources. We mentioned that for the case in which the separation a
>> λ, I12 spatially averages to zero. Why is this true? What
happens when a is much less than λ? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3.
Return to Fig. 2.22 and prove that if two electromagnetic plane waves
making an angle θ have the same amplitude, Eθ, the resulting
interference pattern on the yx-plane is a cosine-squared irradiance..
distribution given by...Locate the zeros of irradiance. What is the
value of the fringe separation? What happens to the separation as θ
increases? Compare your analysis with that leading to Eq. (9.17). [Hint:
Begin with the wave expressions given in Section 2.7, which have the
proper phases already worked out, and write them as exponentials.] <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4.
Will we get an interference pattern in Young's Experiment (Fig. 9.8) if
we replace the source slit S by a single long-filament light-bulb? What
would occur if we replaced the slits S1, and S2 by these same bulbs? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5.
Figure P.9.5 shows an output pattern that was measured by a • tiny
microphone when two small piezo-loudspeakers separated by 15 cm were
pointed toward the microphone at a distance of 1.5 m away. Given that
the speed of sound at 20°C is 343 m/s, determine the approximate
frequency at which the speakers were driven. Discuss the nature of the
pattern and explain why it has a central minimum.Figure P.9.5 (Data
courtesy of CENCO.)... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6.
Two 1.0-MHz radio antennas emitting in-phase are separated by 600 m
along a north-south line. A radio receiver placed 2.0 km east is
equidistant from both transmitting antennas and picks up a fairly strong
signal. How far north should that receiver be moved if it is again to
detect a signal nearly as strong? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9.
An expanded beam of red light from a He-Ne laser (λ0 = 632.8nm) is
incident on a screen containing two very narrow horizontal slits
separated by 0.200 mm. A fringe pattern appears on a white screen held
1.00 m away.(a) How far (in radians and millimeters) above and below the
central axis ate the first zeros of irradiance?(b) How far (in mm) from
the axis is die fifth bright band?(c) Compare these two results. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11.
Red plane waves from a ruby laser (λ0 = 694.3nm) in air impinge on two
parallel slits in an opaque screen. A fringe pattern forms on a distant
wall, and we see the fourth bright band 1.0° above the central axis.
Kindly calculate the separation between the slits. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12.
A 3 × 5 card containing two pinholes, 0.08 mm in diameter and separated
center to center by 0.10 mm, is illuminated by parallel rays of blue
light from an argon ion laser (λ0 = 487.99 nm). If the fringes on an
observing screen are to be 10mm apart, how far away should the screen
be? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13.
White light falling on two long narrow slits emerges and is observed on
a distant screen. If red light (λ0 = 780 nm) in the first-order fringe
overlaps violet in the second-order fringe, what is the latter's
wavelength? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16.
Considering the double-slit experiment, derive an equation for the
distance ym from the central axis to the m'th irradiance minimum, such
that the first dark bands on either side of the central maximum
correspond to m' = ±1. Identify and justify all your approximations. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18.
With regard to Young's Experiment, derive a general expression for the
shift in the vertical position of the mth maximum as a result of placing
a thin parallel sheet of glass of index n and thickness d directly over
one of the slits. Identify your assumptions. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19.
Plane waves of monochromatic light impinge at an angle θi on a screen
containing two narrow slits separated by a distance a. Derive" an
equation for the angle measured from the central axis which locates the
mth maximum. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20.
Sunlight incident on a screen containing two long narrow slits 0.20 mm
apart casts a pattern on a white sheet of paper 2.0 m beyond. What is
the distance separating the violet (λ0 = 400 nm) in the first-order band
from the red (λ0 = 600 nm) in the second-order band? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21.
To examine the conditions under which the approximations of H3q. (9.23)
are valid:(a) Apply the law of cosines to triangle S1S2P in Fig. 9.8c
to get...(b) Expand this in a Maclaurin series yielding...(c) In light
of Eq. (9.17), show that if (r1, - r2) is to equal a sin θ, it is
required that r1, >> a2/λ. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22.
A stream of electrons, each having an energy of 0.5 eV, impinges on a
pair of extremely thin slits separated by 10-2mm. What is the distance
between adjacent minima on a screen 20 m behind the slits? (me, = 9.108 ×
10-31kg, 1 eV = 1.602 × 10-19J.) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23.
It is our intention to produce interference fringes by illuminating
some sort of arrangement (Young's Experiment, a thin film, the Michelson
Interferometer, etc.) with light at a mean wavelength of 500 nm, having
a linewidth of 2.5 X 10-3 nm. At approximately what optical path length
difference can you expect the fringes to vanish? [Hint: Think about the
coherence length and revisit Problem 7.39.] <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24.
Imagine that you have an opaque screen with three horizontal 1 very
narrow parallel slits in it. The second slit is a center-to-center
distance a beneath the first, and the third is a distance 5a/2 beneath
the first, (a) Write a complex exponential expression in terms of δ for
the amplitude of the electric field at some point P at an elevation θ on
a distant screen where δ = ka sin θ. Prove that...Verify that at θ
=0,I(θ) = I (0). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26.
In the Fresnel double mirror s = 2 m, λ0 = 589 nm, and the separation
of the fringes was found to be 0.5 mm. What is the angle of inclination
of the mirrors, if the perpendicular distance of the actual point source
to the intersection of the two mirrors is I m? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27. Show that a for the Fresnel biprism of Fig. 9.13 is given by a = 2d(n - l)α. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28.
The Fresnel biprism is used to obtain fringes from a point source that
is placed 2 m from the screen, and the prism is midway between the
source and the screen. Let the wavelength of the light be λ0 = 500 nm
and the index of refraction of the glass be n = 1.5. What is the prism
angle, if the separation of the fringes is 0.5 mm? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29.
What is the general expression for the separation of the fringes of a
Fresnel biprism of index n immersed in a medium having an index of
refraction n'? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31.
Using Lloyd's mirror, X-ray fringes were observed, the spacing of which
was found to be 0.ÖÖ2 5 cm. The wavelength used was 8.33 Ǻ. If the
source-screen distance was 3 m, how high above the min or plane was the
point source of X-rays placed? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32.
Imagine that we have an antenna at the edge of a lake picking up a
signal from a distant radio star (Fig. P.9.24), which is just coming up
above the horizon. Write expressions for δ and for the angular position
of the star when the antenna detects its first maximum.Figure P.9.24... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33.
If the plate in Fig. 9.17 is glass in air, show that the amplitudes of
Elr, E2r, and E3r are respectively 0.2 E0i, 0.192 E0i. and 0.008E0i
where E0i is the incident amplitude. Make use of the Fresnel
coefficients at normal incidence, assuming no absorption. You might
repeal the calculation for a water film in air. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34.
A soap film surrounded by air has an index of refraction of 1.34. If a
region of the film appears bright red (λ0 = 633 nm) in normally
reflected light, what is its minimum thickness there? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />35.
A thin film of ethyl alcohol (n = 1.36) spread on a flat glass plate
and illuminated with white light shows a color pattern in reflection. If
a region of the film reflects only green light (500 nm) strongly, how
thick is it? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.35p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />36.
A soap film of index 1.34 has a region where it is 550.0 nm thick.
Detennine the vacuum wavelengths of the radiation that is not reflected
when the film is illuminated from above with sunlight. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.36p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />37. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.37p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />38.
Consider the circular pattern of Haidinger's fringes resulting from a
film with a thickness of 2 mm and an index of refraction of 1.5. For
monochromatic illumination of λ0 = 600 nm, find the value of m for the
central fringe (θt, = 0). Will it be bright or dark? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.38p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />39.
Illuminate a microscope slide (or even belter, a thin cover-glass
slide). Colored fringes can easily be seen with an ordinary fluorescent
lamp (although some of the newer versions don't work well at all)
serving as a broad source or a mercury street light as a point source.
Describe the fringes. Now rotate the glass. Does the pattern change?
Duplicate the conditions shown in Figs. 9.18 and 9.19. Try it again with
a sheet of plastic food wrap stretched across the lop of a cup. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.39p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />40.
Fringes are observed when a parallel beam of light of wavelength 500 nm
is incident perpendicularly onto a wedge-shaped film with an index of
refraction of 1.5. What is the angle of the wedge if the fringe
separation is ... cm?Figure P.9.31... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.40p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />41.
Suppose a wedge-shaped air film is made between two sheets of glass,
with a piece of paper 7.618 X 10-5 m thick used as the spacer at their
very ends. If light of wavelength 500 nm comes down from directly above,
determine the number of bright fringes that will be seen across the
wedge. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.41p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />42. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.42p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />43.
Figure P.9.31 illustrates a setup used for testing lenses. Show thatd =
x2(R1 – R1,)/2R1R2when d1 and d2 are negligible in comparison with 2R1,
and 2R2, respectively. (Recall the theorem from plane geometry that
relates the products of the segments of intersecting chords.) Prove that
the radius of the mth dark fringe is then...How does this relate to Eq.
(9.43)? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.43p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />44.
Newton rings are observed on a film with quasimonochromatic that has a
wavelength of 500 nm. If the 20th bright ring has a radius of 1 cm, what
is the radius of curvature of the lens forming one part of the
interfering system? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.44p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />45. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.45p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />46. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.46p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />47. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.47p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />48.
One of the mirrors of a Michelson Interferometer is moved, and 1000
fringe-pairs shift past the hairline in a viewing telescope during the
process. If the device is illuminated wilh 500-nm light, how far was the
mirror moved? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.48p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />49. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.49p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />50.
Suppose we place a chamber 10.0 cm long with flat parallel windows in
one arm of a Michelson Interferometer that is being illuminated by
600-nm light. If the refractive index of air is 1.000 29 and all the air
is pumped out of the cell, how many fringe-pairs will shift by in the
process? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.50p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />51. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.51p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />52. A form of the Jamin Interferometer is illustrated in Fig. P.9.38. How does it work? To what use might it be put? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.52p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />53. Starting with Eq. (9.53) for the transmitted wave, compute the flux density, thai is, Eq. (9.54). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.53p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />54.
Given that the mirrors of a Fabry-Perol Interferometer have
an...amplitude reflection coefficient of r = 0.8944, find(a) the
coefficient of finesse,(b) the half-width,(c) the finesse, and,(d) the
contrast factor defined by... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.54p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />55.
To fill in some of the details in the derivation of the smallest phase
increment separating two resolvable Fabry-Perot fringes, that
is,...satisfy yourself that...Show that Eq. (9.72) can be rewritten
as...When F is large γ is small, and sin (∆δ) = ∆δ. Prove that Eq.
(9.73) then follows. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.55p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />56.
Consider the interference pattern of the Michelson Interferometer as
arising from two beams of equal flux density. Using Eq.(9.17), compute
the half-width. What is the separation, in S, between adjacent maxima?
What then is the finesse? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.56p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />57.
Satisfy yourself of the fact that a film of thickness λf/4 and index
n1, will always reduce the reflectance of the substrate on which it is
deposited, as long as ns, > n1, >n0. Consider the simplest case of
normal incidence and n0 = 1. Show that this is equivalent to saying
that the waves reflected back from the two interfaces cancel one
another. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.57p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />58.
Verify that the reflectance of a substrate can be increased by coating
it with a λf/4, high-index layer, that is, n1 > ns* Show that the
reflected waves interfere constructively. The quarter-wave stack
g(HL)"'Ha can be thought of as a series of such structures. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.58p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />59.
Determine the refractive index and thickness of a film to be deposited
on a glass surface (ng = 1.54) such that no normally incident light of
wavelength 540 nm is reflected. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.59p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />60.
A glass microscope lens having an index of 1.55 is to be coated with a
magnesium fluoride film to increase the transmission of normally
incident yellow light (λ0 = 550 nm). What minimum thickness should be
deposited on the lens? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.60p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />61.
A glass camera lens with an index of 1.55 is to be coated with a
cryolite film (n ≈ 1.30) to decrease the reflection of normally incident
green light (λ0 = 500 nm). What thickness should be deposited on the
lens? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.61p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />62.
Using Fig. 9.60, which depicts the geometry of the Shuttle -radar
interferometer, show thatz(x) = h – r1, cos θThen use (he Law of Cosines
to establish that Eq. (9.108) is correct. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=9.62p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-3424298093127499042020-07-03T13:49:00.001-07:002020-07-03T13:49:08.227-07:00Chapter #8 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4. Describe completely the state of polarization of each of the following waves:(a) ... (b) ...(c) ...(d) ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5.
Consider the disturbance given by the expression ... (z, t) = ... E0
sin kz. What kind of wave is it? Draw a rough sketch showing its main
features. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6.
Analytically, show that the superposition of an... and an...instate
having different amplitudes will yield an ...state, as shown in Fig.
8.8. What must e be to duplicate that figure? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7.
Write an expression for a ...state lightwave of angular frequency ω and
amplitude E0 propagating along the .r-axis with its plane of vibration
at an angle of 25° to the xy-plane. The disturbance is zero at t = 0 and
x = 0. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8.
Write an expression for a ...state lightwave of angular frequency ω and
amplitude E0 propagating along a line in the xy-plane at 45° to the
x-axis and having its plane of vibration corresponding to the .xy-plane.
At t = 0, y = 0, and x = 0 the field is zero. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9.
Write an expression for an ... state lightwave of frequency co
propagating in the positive x-direction such that at t = 0 and x = 0 the
...-field points in the negative z-direction. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10.
A beam of linearly polarized light with its electric field vertical
impinges perpendicularly on an ideal linear polarizer with a vertical
transmission axis. If the incoming beam has an irradiance of 200-W/m2,
what is the irradiance of the transmitted beam? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11.
Given that 300 W/m2 of light from an ordinary tungsten bulb arrives at
an ideal linear polarizer. What is its radiant flux density on emerging?
<a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12.
A beam of vertically polarized linear light is perpendicularly incident
on an ideal linear polarizer. Show that if its transmission axis makes
an angle of 60° with the vertical only 25% of the irradiance will be
transmitted by the polarizer. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15.
If light that is initially natural and of flux density Ii; passes
through two sheets of HN-32 whose transmission axes are parallel, what
will be the flux density of the emerging beam? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16. What will be the irradiance of the emerging beam if the analyzer of the previous problem is rotated 30°? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18.
The irradiance of a beam of natural light is 400 W/m2. It impinges on
the first of two consecutive ideal linear polarizers whose transmission
axes are 40.0° apart. How much light emerges from the two? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22.
As we saw in Section 8.10, substances such as sugar and insulin are
optically active; they rotate the plane of polarization in proportion to
both the path length and the concentration of the solution. A glass
vessel is placed between a pair of crossed HN-50 linear polarizers, and
50% of the natural light incident on the first polarizer is transmitted
through the second polarizer. By how much did the sugar solution in the
cell rotate the light passed by the first polarizer? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23.
The light from an ordinary flashlight is passed through a linear
polarizer with its transmission axis vertical. The resulting beam,
having an irradiance of 200 W/m2, is incident normally on a vertical
HN-50 linear polarizer whose transmission axis is tilted al 30° above
the horizontal. How much light is transmitted? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24.
Linearly polarized light (with an irradiance of 200 W/m2) aligned with
its electric-field vector at +55˚ from the vertical impinges
perpendicularly on an ideal sheet polarizer whose transmission axis is
at +10° from the vertical. What fraction of the incoming light emerges? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25.
Two ideal linear sheet polarizers are arranged with respect to the
vertical with their transmission axis at 10° and 60°, respectively. If a
linearly polarized beam of light with its electric field at 40° enters
the first polarizer, what fraction of its irradiance will emerge? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26.
Imagine a pair of crossed polarizers with transmission axes vertical
and horizontal. The beam emerging from the first polarizer has flux
density I1, and of course no light passes through the analyzer (i.e., I2
= 0). Now insert a perfect linear polarizer (HN-50) with its
transmission axis at 45° to the vertical between the two elements—
compute I2- Think about the motion of the electrons that arc radiating
in each polarizer. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27.
Imagine that you have two identical perfect linear polarizers and a
source of natural light. Place them one behind the other and position
their transmission axes at 0° and 50°, respectively. Now insert between
(hem a third linear polarizer with its transmission axes at 25°. If 1000
W/m2 of light is incident, how much will emerge with and without the
middle polarizer in place? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28.
Given that 200 W/m2 of randomly polarized light is incident normally on
a stack of ideal linear polarizers that are positioned one behind the
other with the transmission axis of the first vertical, the second at
30", the third at 60", and the fourth at 90°. How much light emerges? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29.
Two HN-50 linear polarizers are positioned one behind the other. What
angle should their transmission axes make if an incident unpolarized
100-W/m2 beam is to be reduced to 30.0 W/m2 on emerging from the pan'? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30.
An ideal polarizer is rotated at a rate co between a similar pair of
stationary crossed polarizers. Show that the emergent flux density will
be modulated at four tunes the rotational frequency. In other words,
show that...where I1, is the flux density emerging from the first
polarizer and I is the final flux density. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31.
Figure P.8.22 shows a ray traversing a calcite crystal at nearly normal
incidence, bouncing off a mirror, and then going through the crystal
again. Will the observer see a double image of the spot on ...?... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32.
A pencil mark on a sheet of paper is covered by a calcite crystal. With
illumination from above, isn't the light impinging on the paper already
polarized, having passed through the crystal? Why then do we see two
images? Test your solution by polarizing the light from a flashlight and
then reflecting it off a sheet of paper. Try specular reflection off
glass; is the reflected light polarized? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33.
Discuss in detail what you see in Fig. P.8.24. The crystal in the
photograph is calcite, and it has a blunt corner at the upper left. The
two Polaroids have their transmission axes parallel to their short
edges.... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34.
The calcite crystal in Fig. P.8.25 is shown in three different
orientations. Its blunt comer is on the left in (a), the lower left in
(b), and the bottom in (c). The Polaroid's transmission axis is
horizontal. Explain each photograph, particularly (b). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />35.
in discussing calcite, we pointed out that its large birefringence
arises from the fact that the carbonate groups lie in parallel
planesa...b...c...(normal to the optic axis). Show in a sketch and
explain why the polarization of the group will be less when ... is
perpendicular to the C03 plane than when ... is parallel to it. What
does this mean with respect to v± and vn, that is, the wave's speeds
when ... is linearly polarized perpendicular or parallel to the optic
axis? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.35p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />36.
A beam of light enters a calcite prism from the left, as shown in Fig.
P.8.36. There are three possible orientations of the optic axis of
particular interest, and these correspond to the X-, y-, and
z-directions. Imagine that we have three such prisms. In each case
sketch the entering and emerging beams, showing the state of
polarization. How can any one of these be used to determine n0 and
ne1... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.36p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />37.
Compute the critical angle for the ordinary ray, that is, the angle for
total internal reflection at the calcite-balsam layer of a Nicol prism.
<a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.37p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />38. Draw a quartz Wollaston prism, showing all pertinent rays and their polarization states. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.38p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />39. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.39p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />40.
The prism shown in Fig. P.8.40 is known as a Rochon polarizer. Sketch
all the pertinent rays, assuming(a) that it is made of calcite.(b) that
it is made of quartz.(c) Why might such a device be more useful than a
dichroic polarizer when functioning with high-flux density laser
light?(d) What valuable feature of the Rochon is lacking in the
Wollaston polarizer? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.40p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />41.
Imagine that we have a transmitter of microwaves that radiates a
linearly polarized wave whose ...-field is known to be parallel to the
dipole direction. We wish to reflect as much energy as possible off the
surface of a pond (having an index of refraction of 9.0). Find the
necessary incident angle and comment on the orientation of the beam. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.41p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />42.
At what angle will the reflection of the sky coming off the surface of a
pond (n = 1.33) completely vanish when seen through a Polaroid filter? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.42p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />43.
What is Brewster's angle for reflection of light from the surface of a
piece of glass (ng = 1.65) immersed in water (nw = 1.33)? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.43p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />44. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.44p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />45.
A beam of light is reflected off the surface of some unknown liquid,
and the light is examined with a linear sheet polarizer. It is found
that when the central axis of the polarizer (that is, the perpendicular
to the plane of the sheet) is tilted down from the vertical at an angle
of 54.30°, the reflected light is completely passed, provided the
transmission axis is parallel to the plane of the interface. From this
information, compute the index of refraction of the liquid. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.45p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />46.
Light reflected from a glass (ng = 1.65) plate immersed in ethyl
alcohol (ne = 1.36) is found to be completely linearly polarized. At
what angle will the partially polarized beam be transmitted into the
plate? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.46p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />47.
A beam of natural light is incident on an air-glass interface (nti =
1.5) at 40˚. Compute the degree of polarization of the reflected light. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.47p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />48. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.48p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />49.
A beam of natural light incident in air on a glass (n = 1.5) interface
at 70° is partially reflected. Compute the overall reflectance. How
would this compare with the case of incidence at, say, 56.3°? Explain. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.49p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />50. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.50p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />51. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.51p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />52.
A ray of yellow light is incident on a calcite plate at 50°. The plate
is cut so that the optic axis is parallel to the front face and
perpendicular to the plane-of-incidence. Find the angular separation
between the two emerging rays. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.52p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />53.
A beam of light is incident normally on a quartz plate whose optic axis
is perpendicular to the beam, If λ0 = 589.3 nm, compute the wavelengths
of both the ordinary and extraordinary waves. What are their
frequencies? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.53p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />54.
The electric-field vector of an incident ...state makes an angle of+30°
with the horizontal fast axis of a quarter-wave plate. Describe, in
detail, the state of polarization of the emergent wave. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.54p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />55.
Take two ideal Polaroids (the first with its axis vertical and the
second, horizontal) and insert between them a stack of 10 half-wave
plates, the first with its fast axis rotated π/40 rad from the vertical,
and each subsequent one rotated π/40 rad from the previous one.
Determine the ratio of the emerging to incident irradiance, showing your
logic clearly. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.55p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />56.
Suppose you were given a linear polarizer and a quarter-wave plate. How
could you determine which was which, assuming you also had a source of
natural light? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.56p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />57. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.57p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />58. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.58p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />59. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.59p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />60. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.60p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />61. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.61p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />62. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.62p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />63. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.63p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />64. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.64p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />65. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.65p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />66. An ... state traverses an eighth-wave plate having a horizontal fast axis. What is its polarization state on emerging? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.66p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />67.
Figure P.8.44 shows two Polaroid linear polarizers and between them a
microscope slide to which is attached a piece of cellophane tape.
Explain what you see.... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.67p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />68.
Imagine that we have randomly polarized room light incident almost
normally on the glass surface of a radar screen. A portion of it would
be specularly reflected back toward the viewer and would thus tend to
obscure the display. Suppose now that we cover the screen with a
right-circular polarizer, as shown in Fig. P.8.46. Trace the incident
and reflected beams, indicating their polarization states. What happens
to the reflected beam?... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.68p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />69.
A Babinet compensator is positioned at 45° between crossed linear
polarizers and is being illuminated with sodium light. When a thin sheet
of mica (indices 1.599 and 1.594) is placed on the compensator, the
black bands all shift by ... of the space separating them. Compute the
retardance of the sheet and its thickness. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.69p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />70.
Is it possible for a beam to consist of two orthogonal incoherent
...-states and not be natural light? Explain. How might you arrange to
have such a beam? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.70p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />71.
The specific rotatory power for sucrose dissolved in water at 20°C (λo =
589.3 nm) is +66.45° per 10 cm of path traversed through a solution
containing 1 g of active substance (sugar) per em of solution. A
vertical ...-state (sodium light) enters at one end of a 1-in tube
containing 1000 cm3 of solution, of which 10 g is sucrose. At what
orientation will the ...-state emerge? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.71p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />72.
On examining a piece of stressed photoelastic material between crossed
linear polarizers, we would see a set of colored bands (isochromatics)
and, superimposed on these, a set of dark bands (iso-clinics). How might
we remove the isoclinics, leaving only the isochromatics? Explain your
solution. Incidentally, the proper arrangement is independent of the
orientation of the photoelastic sample. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.72p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />73.
Consider a Kerr cell whose plates are separated by a distance d. Let ℓ
be the effective length of those plates (slightly different from the
actual length because of fringing of the field). Show that... [8.41] <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.73p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />74.
Compute the half-wave voltage for a longitudinal Pockels cell made of
ADA (ammonium dihydrogen arsenate) at λ0 ≈ 550 nm, where r63 = 5.5 X
10-12 and no = 1.58 <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.74p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />75.
The Jones vector for an arbitrary linearly polarized state at an angle Ɵ
with respect to the horizontal is...Prove that this matrix is in
agreement with the one in Table 8.5 for a. ...-state at +45°. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.75p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />76. Find a Jones vector E2 representing a polarization state orthogonal to...Sketch both of these. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.76p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />77.
Two incoherent light beams represented by (1, 1,0,0) and (3, 0, 0, 3)
are superimposed.(a) Describe in detail the polarization states of each
of these.(b) Determine the resulting Stokes parameters of the combined
beam and describe its polarization state.(c) What is its degree of
polarization?(d) What is the resulting light produced by overlapping the
incoherent beams (1, 1, 0, 0) and (1, -1, 0, 0)? Explain. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.77p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />78.
Show by direct calculation, using Mueller matrices, that a
unit-irradiance beam of natural light passing through a vertical linear
polarizer is converted into a vertical ...-state. Determine its relative
irradiance and degree of polarization. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.78p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />79.
Show by direct calculation, using Mueller matrices, that a
unit-irradiance beam of natural light passing through a linear polarizer
with its transmission axis at +45° is converted into a ...-state al
+45°. Determine its relative irradiance and degree of polarization. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.79p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />80.
Show by direct calculation, using Mueller matrices, that a beam of
horizontal ...-state light passing through a ...λ-plate with its fast
axis horizontal emerges unchanged. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.80p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />81.
Confirm that the matrix...will serve as a Mueller matrix for a
quarter-wave plate with its fast axis at +45°. Shine linear light
polarized at 45° through it. What happens? What emerges when a
horizontal ...-state enters the device? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.81p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />82.
The Mueller matrix...in which C = cos 2α and S = sin 2 α, represents an
arbitrary wave-plate having a retardance ∆φ and a fast axis at an angle
α measured with respect to the horizontal. Use it to derive the matrix
given in the previous problem. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.82p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />83.
Beginning with the Mueller matrix for an arbitrary retarder provided in
the previous problem, show that it agrees with the matrix in Table 8.6
for a quarter-wave plate with a vertical fast axis. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.83p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />84.
Derive the Mueller matrix for a quarter-wave plate with its fast axis
at -45°. Check that this matrix effectively cancels the one ir Problem
8.58, so that a beam passing through the two wave *** successively
remains unaltered. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.84p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />85.
Pass a beam of horizontally polarized '' each one of the Δ-plates in
the two previous the states of the emerging light. Explain which field
component is leading which and how Fig. 8.7 compares with these results.
<a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.85p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />86.
Use Table 8.6 to derive a Mueller matrix for a half-wave plate having a
vertical fast axis. Utilize your result to convert an ... into an ....
Verify that the same wave plate will convert an ... to an -....
Advancing or retarding the relative phase by π/2 should have the same
effect. Check this by deriving the matrix for a half-wave plate with a
horizontal fast axis. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.86p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />87.
Construct one possible Mueller matrix for a right-circular polarizer
made out of a linear polarizer and a quarter-wave plate. Such a device
is obviously an inhomogeneous two-element train and will differ from the
homogeneous circular polarizer of Table 8.6. Test your matrix to
determine that it will convert natural light to an .... Show that it
will pass . ..., as will the homogeneous matrix. Your matrix should
convert instates incident on the input side to . ...., whereas the
homogeneous polarizer will totally absorb them. Verify this. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.87p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />88.
If the Pockets cell modulator shown in Fig. 8.57 is illuminated by
light of irradiance Ii it will transmit a beam of irradiance I, such
that...Make a plot of ItIi, versus applied voltage. What is the
significance of the voltage that corresponds to maximum transmission?
What is the lowest voltage above zero that will cause It to be zero for
ADP (λ0 = 546.1 nm)? How can things be rear-ranged to yield a maximum
value of ItIi for zero voltage? In this new configuration what
irradiance results when V — Vλ/2? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.88p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />89.
Construct a Jones matrix for an isotropic plate of absorbing material
having an amplitude transmission coefficient of t. It might sometimes be
desirable to keep track of the phase, since even if t=1. such a plate
is still an isotropic phase retarder. What is the Jones matrix for a
region of vacuum? What is it for a perfect absorber? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.89p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />90.
Construct a Mueller matrix for an isotropic plate of absorbing material
having an amplitude transmission coefficient of t What Mueller matrix
will completely depolarize any wave without affecting its irradiance?
(It has no physical counterpart.) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.90p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />91.
Keeping Eq. (8.29) in mind, write an expression for the randomly
polarized flux density component (In) of a partially polarized beam in
terms of the Stokes parameters. To check your result, add a randomly
polarized Stokes vector of flux density 4 to an . ... of flux density 1.
Then see if you get In = 4 for the resultant wave. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.91p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />92.
An optical filter can be described by a Jones matrix...Obtain the form
of the emerging light for each of the following incident beams:(a) A
plane polarized beam polarized at angle θ to the horizontal (see Problem
8.52).(b) A left-circularly polarized beam.(c) A right-circularly
polarized beam.(d) From the above, identify the filter and explain how
it could be constructed. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.92p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />93.
An optical Filter can be described by a Jones matrix...(a) Obtain the
form of the emerging beam when the incident light is plane poloarized at
angle θ to the horizontal (see Problem 8.52),(b) Deduce from the result
of part (a) the nature of the filter.(c) Confirm your deduction above
with at least one other test. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.93p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />94. Two linear optical filters have Jones matrices...Identify these filters. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.94p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />95.
A liquid cell containing an optically active sugar solution has a Jones
matrix given by...(a) Determine the polarization of the emerging light
if the incident beam is a horizontal ....(b) Determine the polarization
of the emerging light if the incident beam is a vertical ....(c)
Determine the angle of rotation produced by the optically active
material. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=8.95p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-58366063045242214362020-07-03T13:48:00.007-07:002020-07-03T13:48:55.181-07:00Chapter #7 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. Determine the resultant of the superposition of the parallel
waves E1 = E01 sin (ωt + ε1,) and E2 = E02 sin (ωt + ε2) when ω = 120π,
E0l = 6, E02 = 8, ε1 = 0, and ε2 = π/2. Plot each function and the
resultant. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2.
Considering Section 7.1, suppose we began the analysis to find E = E1 +
E2 with two cosine functions E1 = E01 cos (ωt + α1) and E2 = E02 cos
(ωt + α2). To make things a little less complicated, let E01 — E02 and
α1 =0. Add the two waves algebraically and make use of the familiar
trigonometric identity cos θ + cos φ=2 cos ½(θ + φ) cos ½(θ-Ф) in order
to show that E = E1 cos (ωt + α), where E0=2 E01 cos α2/2 and α = α2/2.
Now show that these same results follow from Eqs. (7.9) and (7.10). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3.
Show that when the two waves of Eq. (7.5) are in-phase, the resulting
amplitude squared is a maximum equal to (E01 + E02)2, and when they are
out-of-phase it is a minimum equal to (E01 – E02)2. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4.
Show that the optical path length, defined as the sum of the products
of the various indices times the thicknesses of media traversed by a
beam, that is, ∑1n1x1 is equivalent to the length of the path in vacuum
that would take the same time for that beam to negotiate. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5.
Answer the following:(a) How many wavelengths of λ0 = 500 nm light will
span a 1-m gap in vacuum?(b) How many waves span the gap when a glass
plate 5 cm thick (n = 1.5) is inserted in the path?(c) Determine the OPD
between the two situations.(d) Verify that ... corresponds to the
difference between the solutions to (a) and (b) above. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6.
Determine the optical path difference for the two waves A and B; both
having vacuum wavelengths of 500 nm, depicted in Fig. p.7.6; the glass
(n = 1.52) tank is filled with water (n=1.33). If the waves start out
in-phase and all the above numbers are exact, find their relative phase
difference at the finishing line.... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7.
Using Eqs. (7.9), (7.10), and (7.11), show that the resultant of the
two wavesE1 = E01 sin [ωt-k(x + Δx)]AndE2=E01 sin (ωt-kx) is... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8. Add the two waves of Problem 7.7 directly to find Eq. (7.17). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9.
Use the complex representation to find the resultant E= E1+E2, whereE1=
E0 cos (kx + ωt) and E2 =-E0 cos (kx — ωt)Describe the composite wave. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10.
Consider the functions E1 = 3 cos ωt and E2 = 4 sin ωt. First prove
that E2 = 4 cos (ωt — π/2). Then, using phasors and referring to Fig.
P.7.10, show that E3=E1 + E2 = 5 cos (ωt-φ); determine φ. Discuss the
values of E3 wherever either E1=0 or E2 = 0. Does E3 lead or lag E1 ?
Explain. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14.
Considering Wiener's experiment (Fig. 7.14) in monochromatic light of
wavelength 550 nm, if the film plane is angled at 1.0° to the reflecting
surface, determine the number of bright bands per centimeter that will
appear on it. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15.
Microwaves of frequency 1010 Hz are beamed directly at a metal
reflector. Neglecting the refractive index of air, determine the spacing
between successive nodes in the resulting standing-wave pattern. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16. A standing wave is given by...Determine [wo waves that can be superimposed to generate it. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18. Imagine that we strike two tuning forks, one with a frequency of 340 Hz, the other 342 Hz. What will we hear? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19.
Use the phasor method, described in conjunction with Fig. 7.17, to
explain how two equal-amplitude waves of sightly different frequencies
generate the beat pattern shown in Fig. 7.16 or Fig. P.7.16a. The curve
in Fig. P.7.16b is.a sketch of the phase of the resultant measured with
respect to one of the constituent waves.Explain its main features. When
is it zero and why? When does the phase change abruptly and why?Figure
P.7.16(a). ...(b). ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20.
As we've seen, Eq. (7.33) describes the beat pattern. Let's now derive a
different version of that expression assuming that the two overlapping
equal-amplitude cosine waves have angular spatial frequencies of kc.+ Δk
and kc- Δk, and angular temporal frequencies of ωc,.+ Δω and ωc- Δω,
respectively. Here kc and ωc. correspond to the central frequencies.
Show that the resultant wave is thenE=2E01 cos (Δkx - ωt) cos (kcx
-ωct)Explain how each term relates back to...Prove that the speed of the
envelope, which is the wavelength of the envelope divided by the period
of the envelope, equals the group velocity, namely, Δω/Δk. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21.
FigureP.7.I8 shows a carrier of frequency ωc being amplitude-modulated
by a sine wave of frequency ωm, that is,E = E0(l + a cos ωmt) cos
ωctShow that this is equivalent to the superposition of three waves of
frequencies ωc, ωc+ ωm, and ωc-ωm. When a number of modulating
frequencies are present, we write E as a Fourier series and sum over all
values of ωm. The terms ωc+ ωm constitute what is called the upper
sideband, and all the ωc- ωm terms form the lower sideband.What
bandwidth would you need in order to transmit the complete audible
range?Figure... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22. Given the dispersion relation ω = ak2, compute both the phase and group velocities. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27. Using the relation l/vg = dk/dv, prove that... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28. In the case of light waves, show that... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29.
The speed of propagation of a surface wave in a liquid of depth much
greater than λ is given by...where g = acceleration of gravity, λ =
wavelength, p - density, Y = surface tension. Compute the group velocity
of a pulse in the long wavelength limit (these are called gravity
waves), <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30. Show that the group velocity can be written as... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31. Show that the group velocity can be written as... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32. With the previous problem in mind prove that... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />35. Determine the group velocity of waves when the phase velocity varies inversely with wavelength. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.35p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />36. Show that the group velocity can be written as ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.36p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />37. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.37p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />38.
For a wave propagating in a periodic structure for which ω(k)=2ω0
sin(Kℓ/2), determine both the phase and group velocities. Write the
former as a sine function. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.38p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />39.
An ionized gas or plasma is a dispersive medium for EM-waves. Given
that the dispersion equation isω2 = ωp2+ c2k2where ωp is the constant
plasma frequency, determine expressions for both the phase and group
velocities and show that vv8 = c2. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.39p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />40.
Using the dispersion equation,...show that the group velocity is given
by...for high-frequency electromagnetic waves (e.g., X-rays). Keep in
mind that since fj are the weighting factors, ∑jfj = 1. What is the
phase velocity? Show that vv8 ≈ r2, <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.40p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />41.
Analytically determine the resultant when the two functions E1 = 2E0
cos ωt and E2 = ½E0 sin 2ωt are superimposed. Draw E1, E2, and E = E1 +
E2. Is the resultant periodic; if so, what is its period in terms of ω? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.41p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />42. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.42p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />43. Show that...where a ≠0,b≠ 0, and a and b are positive integers. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.43p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />44. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.44p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />45. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.45p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />46. Given the function f(x) = A cos (πx/L), determine its Fourier scries. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.46p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />47. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.47p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />48. Take the function f(θ) = θ2 in the interval 0θ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.48p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />49. Show that the Fourier series representation of the function f(θ) = |sin θ| is... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.49p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />50.
Change the upper limit of Eq. (7.59) from ∞ to a and evaluate the
integral. Leave the answer in terms of the so-called sine
integral:...which is a function whose values are commonly tabulated. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.50p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />51. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.51p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />52. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.52p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />53. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.53p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />54.
Write an expression for the transform A(ω) of the harmonic pulse of
Fig. P.7.38. Check that sine u is 50% or greater for values of u roughly
less than π/2. With that in mind, show that Δv Δt ≈ 1, where Δv is the
bandwidth of the transform at half its maximum amplitude. Verify that Δv
Δt ≈ 1 at half the maximum value of the power spectrum as well. The
purpose here is to get some sense of the kind of approximations used in
the discussionFigure P.7.38... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.54p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />55.
Derive an expression for the coherence length (in vacuum) of a
wavetrain that has a frequency bandwidth Δv; express your answer in
terms of the line width Δλ0 and the mean wavelength λ0 of the train. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.55p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />56. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.56p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />57.
Consider a photon in the visible region of the spectrum emitted during
an atomic transition of about 10-8 s. How long is the wave packet?
Keeping in mind the results of the previous problem (if you've done it),
estimate the line width of the packet (λ0 = 500 nm). What can you say
about its monochromaticity, as indicated by the frequency stability? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.57p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />58.
The first* experiment directly measuring the bandwidth of a laser (in
this ease a continuous-wave Pb088Sn012 Te diode laser) was carried out
in 1969. The laser, operating at λ0 = 10 600 nm, was heterodyned with a
C02 laser, and bandwidths as narrow as 54 kHz were observed. Compute the
corresponding frequency stability and coherence length for the
lead-lin-telluridc laser. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.58p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />59.
A magnetic-field technique for stabilizing a He-Ne laser to 2 parts in
1010 has been patented. At 632.8 nm, what would be the coherence length
of a laser with such a frequency stability? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.59p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />60.
Imagine that we chop a continuous laserbeam (assumed to be
monochromatic at λ0 = 632.8 nm) into 0.1 -ns pulses, using some son of
shutter. Compute the resultant line width Δλ, bandwidth, and coherence
length. Find the bandwidth and line width that would result if we could
chop at 1015 Hz. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.60p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />61.
Suppose that we have a filter with a pass band of 1.0 Ä centered at 600
nm, and we illuminate it with sunlight. Compute the coherence length of
the emerging wave. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.61p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />62.
A filter passes light with a mean wavelength of ... If the emerging
wavetrains are roughly 20λ0 long, what is the frequency bandwidth of the
exiting light? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.62p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />63.
Suppose we spread white light out into a fan of wavelengths by means of
a diffraction grating and then pass a small select region of that
spectrum out through a slit. Because of the width of the slit, a band of
wavelengths 1.2 nm wide centered on 500 nm emerges. Determine the
frequency bandwidth and the coherence length of this light. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=7.63p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-14386770448586655432020-07-03T13:48:00.005-07:002020-07-03T13:48:42.798-07:00Chapter #6 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. Work out the details leading to Eq. (6.8) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2.
According to the military handbook M1L-HDBK-141 (23.3.5.3), the Ramsden
eyepiece (Fig. 5.94) is made up of two planar-convex lenses of equal
focal length f' separated by a distance 2f'/3. Determine the overall
focal length f of the thin-lens combination and locate the principal
planes and position of the field stop. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3. Write an expression for the thickness d1 of a double-convex lens such that its focal length is infinite. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5.
Suppose we have a positive meniscus lens of radii 6 and 10 and a
thickness of 3 (any units, as long as you're consistent), with an index
of 1.5. Determine its focal length and the locations of its principal
points (compare with Fig. 6.3). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6.
Prove that if the principal points of a biconvex lens of thickness d1
overlap midway between the vertices, the lens is a sphere. Assume the
lens is in air. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7.
Using Eq. (6.2), derive an expression for the focal length of a
homogeneous transparent sphere of radius R. Locate its principal points.
<a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8.
A spherical glass bottle 20 cm in diameter with walls that are
negligibly thin is filled with water. The bottle is sitting on the back
seat of a car on a nice sunny day. What's its focal length? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9.
With the previous two problems in mind, compute the magnification that
results when the image of a flower 4.0 m from the center of a solid,
clear-plastic sphere with a 0.20-m diameter (and a refractive index of
1.4) is cast on a nearby wall. Describe the image in detail. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10.
A thick glass lens of index 1.50 has radii of+23 cm and+20 cm, so that
both vertices are to the left of the corresponding centers of curvature.
Given that the thickness is 9.0 cm, find the focal length of the lens.
Show that in general R1- R2 = d/3 for such afocal zero-power tenses.
Draw a diagram showing what happens to an axial incident parallel bundle
of rays as it passes through the system. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11.
It is found that sunlight is focused to a spot 29.6 cm from the back
face of a thick lens, which has its principal points H1 at +0.2 cm and
H2 at -0.4 cm. Determine the location of the image of a candle that is
placed 49.8 cm in front of the lens. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12.
Please establish that the separation between principal planes for a
thick glass lens is roughly one-third its thickness. The simplest
geometry occurs with a planar-convex lens tracing a ray from the object
focus. What can you say about the relationship between the focal length
and the thickness for this lens type? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13.
A crown glass double-convex lens, 4.0 cm thick and operating at a
wavelength of 900 nm, has an index of refraction of 3/2. Given that its
radii are 4.0 cm and 15 cm, locate its principal points and compute its
focal length. If a television screen is placed 1.0 m from the front of
the lens, where will the real image of the picture appear? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14.
Imagine two identical double-convex thick lenses separated by a
distance of 20 cm between their adjacent vertices. Given that all the
radii of curvature are 50, the refractive indices are 1.5, and the
thickness of each lens is 5.0 cm, calculate the combined focal length. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15.
A compound lens is composed of two thin lenses separated by 10 cm. The
first of these has a focal length of +20 cm, and the second a focal
length of -20 cm. Determine the focal length of the combination and
locate the corresponding principal points. Draw a diagram of the system.
<a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16.
A convex-planar lens of index 3/2 has a thickness of 1.2 cm and a
radius of curvature of 2.5 cm. Determine the system matrix when light is
incident on the curved surface. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20.
A positive meniscus lens with an index of refraction of 2.4 is immersed
in a medium of index 1.9. The lens has an axial thickness of 9.6 mm and
radii of curvature of 50.0 mm and 100 mm. Compute the system matrix
when light is incident on the convex face and show that its determinant
is equal to 1. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21. Prove that the determinant of the system matrix in Eq. (6.31) is equal to 1. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22. Establish that Eqs. (6.36) and (6.37) are equivalent to Eqs. (6.3) and (6.4), respectively. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23. Show that the planar surface of a concave-planar or convex-planar lens doesn' I contribute to the system matrix. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24.
Compute the system matrix for a thick biconvex lens of index 1.5 having
radii of 0.5 and 0.25 and a thickness of 0.3 (in any units you like).
Check that ... = 1. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25.
The system matrix for a thick biconvex lens in air is given
by...Knowing that the first radius is 0.5 cm, that the thickness is 0.3
cm, and that the index of the lens is 1.5, find the other radius. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27.
A concave-planar glass (n =1.50) lens in air has a radius of 10.0 cm
and a thickness of 1.00 cm. Determine the system matrix and check that
its determinant is 1. At what positive angle (in radians measured above
the axis) should a ray strike the lens at a height of 2.0 cm, if it is
t0 emerge from the lens at the same height but parallel to the optical
axis? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28.
Considering the lens in Problem 6.20, determine its focal length and
the location of the focal points with respect to its vertices V1and V2. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29.
Figure P.6.24 shows two identical concave spherical mirrors forming a
so-called confocal cavity. Show, without first specifying the value of
d, that after traversing the cavity two times the system matrix
is...Then for the specific case of d =r show that after four reflections
the system is back where it started and the light will retrace its
original path....Figure P.6.24 <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30. Referring back to Fig. 6.17A, show that when ... and ... all rays originating at P appear to come from P'. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31.
Starting with the exact expression given by Eq. (5.5), show that Eq.
(6.40) results, rather than Eq. (5.8), when the approximations for ℓ0
and ℓ1 are improved a bit. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32.
Supposing that Fig. P.6.27 is to be imaged by a lens system suffering
spherical aberration only, make a sketch of the image....Figure P.6.27 <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33.
Figure P.6.28 shows the image irradiance distributions arising when a
monochromatic point source illuminates three different optical systems,
each having only one type of aberration. From the graphs identify that
aberration in each case and justify your answer....Figure
P.6.28a...Figure P.6.28b...Figure P.6.28c <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34.
Figure P.6.29 shows the distribution of light corresponding i the image
arising when a monochromatic point source illuminates two different
optical systems each having only one type of aberration Identify the
aberration in each case and justify your answerFigure P.6.29(a). ...(b).
... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=6.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-2150439272261144772020-07-03T13:48:00.003-07:002020-07-03T13:48:30.300-07:00Chapter #5 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. The shape of the interface pictured in Fig. P.5.1 is known as a
Cartesian oval after Rene Descartes who studied it in the early 1800s.
It's the perfect configuration to carry any ray from S to the interface
to P. Prove that the defining equation isℓ0n1 + ℓin2 = constantShow that
this is equivalent ton1(x2+y2)1/2+n2[y2+(s0+si-x2)]1/2 = constantFigure
P.5.1... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2.
Construct a Cartesian oval such that the conjugate points will be
separated by 11 cm when the object is 5 cm from the vertex. If n1 | = 1
and n2 = 3/2 draw several points on the required surface. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3.
Use Fig. P.5.3 to show that if a point source is placed at the focus Fv
of the ellipsoid, plane waves will emerge from the far side. Remember
that the defining requirement for an ellipse is that the net distance
from one focus to the curve and back to the other focus is
constant.Figure P.5.3... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4.
Diagrammatically construct both a sphero-clliptic positive lens and an
elliplo-spheric negative lens, showing rays and wavefronts as they pass
through the lens. Do the same for an oval-spheric positive lens. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5.
Making use of Fig. P.5.5, Snell's Law, and the fact that in the
paraxial region α = h/s0, φ ≈ h/R, and β ≈ h/si derive Eq. (5.8).Figure
P.5.5... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6.
Show that, in the paraxial domain, the magnification produced by a
single spherical interface between two continuous media, as shown in
Fig'. P.5.6, is given by...Use the small-angle approximation for Snell's
Law and approximate the angles by their tangents.Figure P.5.6... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7.
Imagine a hemispherical interface, with a radius of curvature of radius
5.00 cm, separating two media: air on the left, water on the right. A
3.00-cm-tall toad is on the central axis, in air, facing the convex
interface and 30.0 cm from its vertex. Where in the water will it Re
imaged? How big will it appear to a fish in the water? Use the results
of the previous problem, even though our frog is pushing the paraxial
approximation. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8.
Locate the image of an object placed 1.2 m from the vertex of a gypsy's
crystal ball, which has a 20-cm diameter (n1 = 1.5). Make a sketch (of
the rays, not the gypsy). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9.
Return to Problem 5.7 and suppose we cut off the medium on the right
foiTning a thick water biconvex lens, with each surface having a radius
of curvature of 5.00 cm. If the lens is 10.0 cm thick, determine the
total magnification and everything you can about the toad's image. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10.
A biconvex glass (n1 = 1.5) thin lens is to have a +10.0-cm focal
length. If the radius of curvature of each surface is measured to 'be
the same, what must it be? Show that a spider standing 1.0 cm frcm the
lens will be imaged at -1.1 cm. Describe that image and draw a ray
diagram. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11.
Going back to Section 5.2.3, prove that for a thin lens mmersed in a
medium of index nm....That done, imagine a double-concave air lens
surrounded by water; determine if it's converging or diverging. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12.
A meniscus concave glass (nl = 1.5) thin lens (see Fig. 5.12) has radii
of curvature of +20.0 cm and +10.0 cm. If an object is placed 20.0 cm
in front of the lens, show that the image distance will be -13.3 cm.
Describe that image and draw a ray diagram. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13.
A biconcave lens (n1, = 1.5) has radii of 20 cm and 10 cm and an axial
thickness of 5 cm. Describe the image of an object 1-inch tall placed 8
cm from the first vertex. Use the thin-lens equation to see how far off
it is in determining the final-image location. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14.
A 35-mm camera has a single thin lens having a 50.0-mm focal length. A
woman 1.7 m tall stands 10.0 m in front of the camera, (a) Show that the
lens-film distance must be 50.3 mm. (b) How tall is her image on the
film? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15. Prove that the minimum separation between conjugate real object and image points for a thin positive lens is 4f. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16.
An object 2 cm high is positioned 5 cm to the right of a positive thin
lens with a focal length of 10 cm. Describe the resulting image
completely, using both the Gaussian and Newtonian equations. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17.
Make a rough graph of the Gaussian Lens Equation; that is, plot Si
versus s0, using unit intervals of f along each axis. (Get both segments
of the curve.) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18.
A parallel bundle of rays from a very distant point source is incident
on a thin negative lens having a focal length of -50.0 cm. The rays make
an angle of 6.0° with the optical axis of the lens. Locate the image of
the source. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20.
What must the focal length of a thin negative lens be for it to form a
virtual image 50 cm away (measured from the lens) of an ant located 100
cm away (measured from the lens)? Given that the ant is to the right of
the lens, locate and describe its image. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22.
Compute the focal length in air of a thin biconvex lens (nl = 1.5)
having radii of 20 and 40 cm. Locate and describe the image of an object
40 cm from the lens. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23.
Determine the focal length of a planar-concave lens (nl = 1.5) having a
radius of curvature of 10 cm. What is its power in diopters? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26.
Determine the focal length in air of a thin spherical planar-convex
lens having a radius of curvature of 50.0 mm and an index of 1.50. What,
if anything, would happen to the focal length if the lens were placed
in a tank of water? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30.
We would like to place an object 45 cm in front of a lens and have its
image appear on a screen 90 cm behind the lens. What must be the focal
length of the appropriate positive lens? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31.
The horse in Fig. 5.26 is 2.25 m tall, and it stands with its face 15.0
m from the plane of the thin lens whose focal length is 3.00 m.(a)
Determine the location of the image of the equine nose.(b) Describe the
image in detail—type, orientation, and magnification.(c) How tall is the
image?(d) If the horse's tail is ! 7.5 m from the lens, how long,
nose-to-tail, is the image of the beast? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32.
A candle that is 6.00 cm tall is standing 10 cm from a thin concave
lens whose focal length is —30 cm. Determine the location of the image
and describe it in detail. Draw an appropriate ray diagram. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33.
The image projected by an cquiconvex lens (n = 1.50) of a frog 5.0 cm
tall, who is located 0.60 m from a screen, is to be 25 cm high. Please
compute the necessary radii of the lens. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />35. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.35p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />36. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.36p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />37.
A thin piece of wire 4.00 mm long is located in a plane perpendicular
to the optical axis and 60.0 cm in front of a thin lens. The sharp image
of the wire formed on a screen is 2.00 mm long. What is the focal
length of the lens? When the screen is moved farther from the lens by
10.0 mm, the image blurs to a width of 0.80 mm. What is the diameter of
the lens? [Hint: Image a source point on the axis.] <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.37p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />38.
A thin double-convex glass lens (with an index of 1.56) while
surrounded by air has a 10-cm focal length. If it is placed under water
(having an index of 1.33) 100 cm beyond a small fish, where will the
guppy's image be formed? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.38p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />39.
Consider a homemade television projection system that uses a large
positive lens to cast the image of the TV screen onto a wall. The
projected picture is enlarged three times, and although dim, it's nice
and clear. If the lens has a focal length of 60 cm, what should be the
distance between the screen and the wall? Why use a large lens? How
should we mount the set with respect to the lens? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.39p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />40.
Write an expression for the focal length (fw) of a thin lens immersed
in water (nw = 4/3) in terms of its focal length when it's in air (fa) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.40p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />41.
Observe the three vectors ..., ...and ... in Fig. P.5.31, each of which
has a length of 0.10 f where f is the focal length of the thin positive
lens. The plane formed by ... and ... is at a distance of 1.10 f from
(he lens. Describe the image of each vector.Figure P.5.31... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.41p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />42.
A convenient way to measure the focal length of a positive lens makes
use of the following fact. If a pair of conjugate object and (real)
image points (S and P) are separated by a distance L > 4f, there will
be two locations of the lens, a distance d apart, for which the same
pair of conjugates obtain. Show that...Note that this avoids
measurements made specifically from the vertex, which are generally not
easy to do. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.42p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />43.
Two positive lenses with focal lengths of 0.30 m and 0.50 m are
separated by a distance of 0.20 m. A small butterfly rests on the
central axis 0.50 m in front of the first lens. Locate the resulting
image with respect to the second lens. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.43p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />44.
In the process of constructing a doublet, an equieonvex thin lens L2 is
positioned in intimate contact with a thin negative lens, such that the
combination has a focal length of 50 cm in air. If their indices are
1.50 and 1.55, respectively, and if the focal length of L2 —50 cm,
determine all the radii of curvature. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.44p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />45. Verify Eq. (5.34), which gives MT for a combination of two thin lenses. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.45p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />46.
A blade of grass standing 10.0 mm tall is 150 mm in from of a thin
positive lens having a 100 mm focal length; 250 mm behind that first
lens is a thin negative lens with a focal length of -75.0 mm. (a) Show
that the first lens forms an image 300 mm behind it. (b) Describe that
image, (c) What's its magnification? (d) Prove that the final image
formed by both lenses is located 150 mm belund the negative lens, (e)
What is the total magnification of the combination? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.46p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />47.
Compute the image location and magnification of an object 30 cm from
the front doublet of the thin-lens combination in Fig. P.5.37. Do the
calculation by finding the effect of each lens separately. Make a sketch
of appropriate rays.Figure P.5.37... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.47p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />48.
Two thin lenses having focal lengths of + 15.0 cm and -15.0 cm are
positioned 60.0 cm apart. A page of print is held 25.0 cm in front of
the positive lens. Describe, in detail, the image of the print (i.e.,
insofar as it's paraxial). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.48p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />49.
Draw a ray diagram for the combination of two positive lenses wherein
their separation equals the sum of their respective focal lengths. Do
the same thing for the case in which one of the lenses is negative. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.49p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />50.
Two positive lenses are to be used as a laserbeam expander. An axial
1.0-mm diameter beam enters a short focal length positive lens, which is
followed by a somewhat longer focal length positive lens from which it
emerges with a diameter of 8.0 mm. Given that the first lens has a 50.0
mm focal length, determine the focal length of the second lens and the
separation between the lenses. Draw a diagram. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.50p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />51.
Redraw the ray diagram for a compound microscope (Fig. 5.99), but this
time treat the intermediate image as if it were a real object. This
approach should be a bit simpler. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.51p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />52.
Consider a thin positive lens L1 and using a ray diagram, show that if a
second lens L2 is placed at the focal point of L2, the magnification
does not change. That's a good reason to wear eyeglasses, whose lenses
are different, al the correct distance from the eye. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.52p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />53.
Figures P.5.43a and P.5.43b are taken from an introductory •physics
book. What's wrong with them?Figure P.5.43a...Figure P.5.43b... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.53p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />54. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.54p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />55.
Consider the case of two positive thin lenses, L1, and L2, separated by
5 cm. Their diameters are 6 and 4 cm, respectively, and their focal
lengths are f1 = 9 cm and f2 = 3 cm. If a diaphragm with a hole 1 cm in
diameter is located between them, 2 cm from L2, find (a) the aperture
stop and (b) the locations and sizes of the pupils for an axial point,
S, 12 cm in front of (to the left of) L1. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.55p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />56. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.56p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />57. Make a sketch roughly locating the aperture stop and entrance and exit pupils for the lens in Fig. P.5.45... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.57p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />58.
Make a sketch roughly locating the aperture stop and entrance and exit
pupils for the lens in Fig. P.5.46, assuming the object point to be
beyond (to the left of) F01.Figure P.5.46... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.58p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />59. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.59p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />60. Figure P.5.47 shows a lens system, an object, and the appropri-"ate pupils. Diagrammalically locate the image.... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.60p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />61.
Draw a ray diagram locating the images of a point source as formed by a
pair of mirrors at 90° (Fig. P.5.48a). Now create a ray diagram
locating the images of the arrow shown in Fig. P.5.486.Figure P.5.48a.
...b. ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.61p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />62.
Examine Velasquez's painting of Venus and Cupid (Fig. P.5.49). Is Venus
looking at herself in the mirror? Explain.Figure P.5.49 The Toilet of
Venus by Diego Rodriguez de Silva y Veläquez (Courtesy of the Trustees,
The National Gallery, London)... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.62p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />63.
Manet's painting The Bar at the Folies Bergeres (Fig. P.5.50) shows a
girl standing in front of a large planar mirror. Reflected in it is her
back and a man in evening dress with whom she appears to be talking. It
would seem that Manet's intent was to give the uncanny feeling that the
viewer is standing where that gentleman must be. From the laws of
Geometrical Optics, what's wrong?Figure P.5.50 The Bar at (tie Folies
Bergere by Edouard Manet (Courtesy of the Courtauld Institute Galleries,
London. Courtauld Collection.)... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.63p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />64. Show that Eq. (5.48) for a spherical surface is equally applicable to a plane mirror. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.64p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />65. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.65p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />66. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.66p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />67. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.67p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />68. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.68p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />69. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.69p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />70. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.70p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />71. Locate the image of a paperclip 100 cm away from a convex spherical mirror having a radius of curvature of 80 cm. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.71p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />72.
Imagine that you are standing 5 feet from, and looking directly toward,
a brass ball 1 foot in diameter hanging in front of a pawn shop.
Describe the image you would see in the ball. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.72p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />73.
A thin lens having a focal length of +50.0 cm is positioned 250 cm in
front of (i.e., to the left of) a plane mirror. An ant sits on the
central axis 250 cm in front of (i.e., to the left of) the lens. Locate
the three images of the ant. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.73p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />74.
The image of a red rose is formed by a concave spherical mirror on a
screen 100 cm away. If the rose is 25 cm from the mirror, determine its
radius of curvature. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.74p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />75.
From the image configuration determine the shape of the mirror hanging
on the back wall in van Eyck's painting of John Amulfini and His Wife
(Fig. P.5.56).Figure P.5.56 Detail of John Amolfini and His Wife by Jan
van Eyck. (Courtesy of the Trustees, The National Gallery, London... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.75p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />76. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.76p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />77.
There are several varieties of retro-reflector that are commercially
available; one type is comprised of transparent spheres, the backs of
which arc silvered. Light is refracted at the front surface, focused
onto the rear surface, and there reflected back out in the direction it
came. Determine the necessary index of refraction of the spheres. Assume
the incident light is collimated. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.77p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />78.
Design an eye for a robot using a concave spherical mirror such that
the image of an object 1.0 m tall and 1.0 cm away fills its
1.0-cm-square photosensitive detector (which is movable for focusing
purposes). Where should this detector be located with respect to the
mirror? What should be the focal length of the mirror? Draw a ray
diagram. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.78p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />79. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.79p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />80.
Design a little dentist's mirror to be fixed at the end of a shaft for
use in the mouth of some happy soul. The requirements are (1) that the
image be erect as seen by the dentist and (2) that when held 1.5 cm from
a tooth the mirror produces an image twice life-size. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.80p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />81.
An object is located at a distance s0 from a spherical mirror of radius
R. Show that the resulting image will be magnified by an amount... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.81p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />82.
A device used to measure the radius of curvature of the cornea of the
eye is called a keratomeler. This is useful information when tit-ting
contact lenses. In effect, an illuminated object is placed a known
distance from the eye, and the image reflected off the cornea is
observed. The instrument allows the operator to measure the size of that
virtual image. If the magnification is found to be 0.037× when the
object distance is set at 100 mm, what is the radius of curvature? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.82p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />83.
Considering the operation of a spherical mirror, prove that the
locations of the object and image are given bys0 =f(MT - 1)/MT and si =
-f(MT - 1) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.83p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />84.
Aman whose face is 25 cm away looks into the bowl of a soup-spoon and
sees his image reflected with a magnification of —0.064. Determine the
radius of curvature of the spoon. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.84p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />85.
In an amusement park a large upright convex spherical mirror is facing a
plane minor 10.0 m away. A girl 1.0 m tall standing midway between the
two sees herself twice as tall in the plane mirror as in the spherical
one. In other words, the angle subtended at the observer by the image in
the plane mirror is twice the angle subtended by the image in the
spherical mirror. What is the focal length of the latter? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.85p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />86.
A homemade telephoto "lens" (Fig. P.5.65) consists of two spherical
mirrors. The radius of curvature is 2.0 m for the primary and 60 em for
the secondary. How far from the smaller mirror should the film plane be
located if the object is a star? What is the effective focal length of
the system?... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.86p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />87.
A point source S sitting on the central axis of a positive thin lens is
located (to the left) between one and two focal lengths from the lens. A
concave spherical mirror is to be positioned to the right of the lens
so that the final real image also lies at point S. Where should the
mirror be placed? Where should a convex spherical mirror be located to
accomplish the same feat? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.87p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />88.
Suppose you have a concave spherical mirror with a focal length of 10
cm. At what distance must an object be placed if its image is to be
erect and one and a half times as large? What is the radius of curvature
of the mirror? Cheek with Table 5.5. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.88p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />89.
Describe the image that would result for an object 3 inches tall placed
20 cm from a spherical concave shaving mirror having a radius of
curvature of -60 cm. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.89p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />90. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.90p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />91.
Parallel rays along the central axis enter a biconcave lens, both of
whose radii of curvature are equal. Some of the light is reflected from
the first surface, and the remainder passes through the lens. Show that,
if the index of refraction of the lens (which is surrounded by air) is
2.00, the reflected image will fall at the same point as the image
formed by the lens. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.91p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />92.
Referring to the dove prism in Fig. 5.63, rotate it through 90° about
an axis along the ray direction. Sketch the new configuration and
determine the angle through which the image is rotated. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.92p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />93.
Determine the numerical aperture of a single clad optical fiber given
that the core has an index of 1.62 and the clad 1.52. When immersed in
air, what is its maximum acceptance angle? What would happen to a ray
incident at, say, 45°? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.93p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />94. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.94p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />95.
Given a fused silica fiber with an attenuation of 0.2 dB/km how far can
a signal travel along it before the power level drops by half? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.95p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />96. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.96p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />97. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.97p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />98. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.98p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />99. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.99p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />100.
Determine the intermodal delay (in us/km) for a stepped-index fiber
with a cladding of index 1.485 and a core of index 1.500. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.100p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />101.
Using the information on the eye in Section 5.7.1, compute the
approximate size (in milhmeters) of the image of the Moon as cast on the
retina. The Moon has a diameter of 2160 miles and is roughly 230 000
miles from here, although tins, of course, varies. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.101p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />102.
Figure P.5.76 shows an arrangement in which the beam is deviated
through a constant angle σ, equal to twice the angle β between the plane
mirrors, regardless of the angle-of-incidence. Prove that this is
indeed the case.Figure P.5.76... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.102p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />103.
An object 20 m from the objective (f0 = 4 m) of an astronomical
telescope is imaged 30 cm from the eyepiece (/;, = 60 cm). Find the
total linear magnification of the scope. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.103p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />104.
Figure P.5.78, which purports to show an erecting lens system, is taken
from an old, out-of-print optics text. What's wrong with it?... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.104p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />105.
Figure P.5.79 shows a pin hole in an opaque screen being used for
something practical. Explain what's happening and why it works. Try
it.Figure P.5.79... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.105p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />106.
If a photograph of a moving merry-go-round is perfectly exposed, but
blurred, at ... s and f/11, what must the diaphragm setting be if the
shutter speed is raised to ...s in order to "stop" the motion? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.106p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />107.
The field of view of a simple two-element astronomical telescope is
restricted by the size of the eye-lens. Make a ray sketch showing the
vignetting that arises. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.107p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />108.
A field-lens, as a rule, is a positive lens placed at (or near) the
intermediate image plane in order to collect the rays that would
otherwise miss the next lens in the system. In effect, it increases the
field of view without changing the power of the system. Redraw the ray
diagram of the previous problem to include a field-iens. Show that as a
consequence the eye relief is reduced somewhat. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.108p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />109.
Describe completely the image that results when a bug sits at the
vertex of a thin positive lens. How does this relate directly to the
manner in which a field-lens works? (See Problem 5.82.) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.109p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />110.
It is determined that a patient has a near point at 50 cm. If the eye
is approximately 2.0 cm long(a) How much power does the refracting
system have when focused on an object at infinity? when focused at 50
cm?(b) How much accommodation is required to see an object at a distance
of 50 cm?(c) What power must the eye have to see clearly an object at
the standard near-point distance of 25 cm?(d) How much power should be
added to the patient's vision system by a correcting lens? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.110p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />111.
An optometrist finds that a farsighted person has a near point at 125
cm. What power will be required for contact lenses if they are
effectively to move that point inward to a more workable distance of 25
cm so that a book can be read comfortably? Use the fact that if the
object is imaged at the near point, it can be seen clearly. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.111p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />112. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.112p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />113. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.113p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />114. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.114p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />115. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.115p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />116. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.116p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />117.
A farsighted person can see very distant mountains with relaxed eyes
while wearing +3.2-D contact lenses. Prescribe spectacle lenses that
will serve just as well when worn 17 mm in front of the cornea. Locate
and compare the far* point in both cases. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.117p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />118.
A jeweler is examining a diamond 5.0 mm in diameter with a loupe having
a focal length of 25.4 mm.(a) Determine the maximum angular
magnification of the loupe.(b) How big does the stone appeal- through
the magnifier?(c) What is the angle subtended by the diamond at the
unaided eye when held at the near point?(d) What angle does it subtend
at the aided eye? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.118p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />119.
Suppose we wish to make a microscope (that can be used with a relaxed
eye) out of two positive lenses, both with a focal length of 25 mm.
Assuming the object is positioned 27 mm from the objective, (a) how far
apart should the lenses be, and (b) what magnification can we expect? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.119p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />120.
Figure P.5.89 shows a glancing-incidcnce X-ray focusing system designed
in 1952 by Hans Wolter. How does it work? Microscopes with this type of
system have been used to photograph, in X-rays, the implosion of fuel
pellet targets in laser fusion research. Similar X-ray optical
arrangements have been used in astronomical telescopes (see photos on p.
79).Figure P.5.89(a) ...(b) ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.120p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />121.
The two glancing-incidence aspherical mirror systems depicted in Fig.
P.5.90 are designed to focus X-rays. Explain how each works: identify
the shapes of the mirrors, discuss the locations of their various foci,
and so on.Figure P.5.90(a)...(b) ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.121p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />122.
The orbiting Hubble Space Telescope has a 2.4-m primary, which we will
assume to be diffraction limited. Suppose we wanted to use it to read
the print on the side of a distant Russian satellite. Assuming that a
resolution of 1.0 cm at the satellite will do, how far away could it be
from the HST? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=5.122p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-80394552720676229712020-07-03T13:48:00.001-07:002020-07-03T13:48:17.518-07:00Chapter #4 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. Work your way through an argument using dimensional analysis to
establish the λ-4 dependence of the percentage of light scattered in
Ilayleigh Scattering. Let E0i and E0s be the incident and scattered
amplitudes, the latter at a distance r from the scatterer. Assume E0s cc
E0i and E0s α 1/r. Furthermore, plausibly assume that the scattered
amplitude is proportional to the volume, V, of the scatterer; within
limits this is reasonable. Determine the units of the constant of
proportionality. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2.
A white floodlight beam crosses a large volume containing a tenuous
molecular gas mixture of mostly oxygen and nitrogen. Compare the
relative amount of scattering occurring for the yellow (580 nm)
component with that of the violet (400 nm) component. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3.
Figure P.4.3 depicts light emerging from a point source. It shows three
different representations of radiant energy streaming outward. Identify
each one and discuss its relationship to the others.Figure P.4.3 A
segment of a spherical wave... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4.
The equation for a driven damped oscillator is...(a) Explain the
significance of each term.(b) Let ... where E0 and x0 are real
quantities. Substitute into the above expression and show that...(c)
Derive an expression for the phase lag, α, and discuss how α varies as
to goes from ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5.
Imagine that we have a non absorbing glass plate of index n and
thickness Δy, which stands between a source S and an observer P.(a) If
the unobstructed wave (without the plate present) is Eu = E0 exp iω(t –
y/c) show that with the plate in place the observer sees a wave...(b)
Show that if either n ≈ 1 or Δy is very small, then...The second term on
the right may be envisioned as the field arising from the oscillators
in the plate. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6.
A very narrow laserbeam is incident at an angle of 58° on a horizontal
mirror. The reflected beam strikes a wall at a spot 5.0 m away from the
point of incidence where the beam hit the mirror. How far horizontally
is the wall from that point of incidence? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7.
On entering the tomb of FRED the Hero of Nod, you find your¬self in a
dark closed chamber with a small hole in a wall 3.0 m up from the floor.
Once a year, on FRED's birthday, a beam of sunlight enters via the
hole, strikes a small polished gold disk on the floor 4.0 m from the
wall and reflects off it, lighting up a great diamond embedded in the
forehead of a glorious statue of FRED, 20 m from the wall. Roughly how
tall is the statue? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8.
Figure P.4.8 shows what's called a corner mirror. Determine the
direction of the exiting ray with respect to the incident ray.Figure
P.4.8... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11. Calculate the transmission angle for a ray incident in air at 30° on a block of crown glass (ng = 1.52). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12.
The construction in Fig. P.4.10 corresponds to. Descartes! s derivation
of the Law of Refraction. Light moves from S to O in the same time it
travels from O to P. Moreover, its transverse momentum is unchanged on
traversing the interface. Use all of this to "derive" Snell's Law.Figure
P.4.10... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14.
Figure P.4.11 is a plot of the sine of the angle-of-incidence versus
the sine of the transmission angle measured as light passed from air
into a more optically dense medium. Discuss the curve. What is the
significance of the slope of the line? Guess at what the dense medium
might be.Figure P.4.11... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15.
A ray of yellow light from a sodium discharge lamp falls on the surface
of a diamond in air at 45°. If at that frequency nd = 2.42, compute the
angular deviation suffered upon transmission. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16.
Given an interface between water ... and glass ... compute the
transmission angle for a beam incident in the water at 45°. If the
transmitted beam is reversed so that it impinges on the interface, show
that θt, — 45°. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17.
A beam of 12-cm planar microwaves strikes the surface of a dielectric
at 45°. If ... compute (a) the wavelength in the transmitting medium,
and (b) the angle θt. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18.
Light of wavelength 600 nm in vacuum enters a block of glass where ng =
1.5. Compute its wavelength in the glass. What color would it appear to
someone embedded in the glass (see Table 3.4)? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19.
A laserbeam impinges on an air-liquid interface at an angle of 55°. The
refracted ray is observed to be transmitted at 40°. What is the
refractive index of the liquid? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20.
An underwater swimmer shines a beam of light up toward the surface. It
strikes the air-water interface at 35°. At what angle will it emerge
into the air? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21. Make a plot of θi- versus θt, for an air-glass boundary where nga — 1.5. Discuss the shape of the curve. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22.
A laserbeam having a diameter D in air strikes a piece of glass (ng) at
an angle θi. What is the diameter of the beam in the glass? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23.
An exceedingly narrow beam of white light is incident at 60.0° on a
sheet of glass 10.0 cm thick in air. The index of refraction for red
light is 1.505 and for violet light it's 1.545. Determine the
approximate diameter of the emerging beam. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26.
A laserbeam impinges on the top surface of a 2.00-cm-thiek parallel
glass (n = 1.50) plate at an angle of 35°. How long is the actual path
through the glass? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27.
Light is incident in the air on an air-glass interface. If the index of
refraction of the glass is 1.70, find the incident angle such that the
transmission angle is to equal ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28.
Suppose that you focus a camera with a close-up bellows attachment
directly down on a letter printed on this page. The letter is then
covered with a 1.00-mm-thick microscope slide (n = 1.55). How high must
the camera be raised in order to keep the letter in focus? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29.
A coin is resting on the bottom of a tank of water (nw = 1.33) LOO m
deep. On top of the water floats a layer of benzene (nb = 1.50), which
is 20.0 cm thick. Looking down nearly perpendicularly, how far beneath
the topmost surface does the coin appear? Draw a ray diagram. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30.
In Fig. P.4.26 the wavefronts in the incident medium match the fronts
in the transmitting medium everywhere on the interface—a concept known
as wavefront continuity. Write expressions for the number of waves per
unit length along the interface in terms of θi; and λi- in one case and
θt, and λt in the other. Use these to derive Snell's Law. Do you think
Snell's Law applies to sound waves? Explain.Figure P.4.26... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31.
With the previous problem in mind, return to Eq. (4.19) and take the
origin of the coordinate system in the plane-of-incidence and on the
interface (Fig. 4.39). Show that that equation is then equivalent to
equating the x-components of the various propagation vectors. Show that
it is also equivalent to the notion of wavefront continuity. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32.
Making use of the ideas of equal transit times between corresponding
points and the orthogonality of rays and wavefronts, derive the law of
reflection and Snell's Law. The ray diagram of Fig. P.4.28 should be
helpful.Figure P.4.28... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33. Starting with Snell's Law, prove that the vector refraction equation has the form... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34.
Derive a vector expression equivalent to the Law of Reflection. As
before, let the normal go from the incident to the transmitting medium,
even though it obviously doesn't really matter. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />35.
In the case of reflection from a planar surface, use Fermat's Principle
to prove that the incident and reflected rays share a common plane with
the normal ûm namely, the plane-of-incidence. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.35p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />36.
Derive the Law of Reflection, θt- = θr by using the calculus to
minimize the transit time, as required by Fermat's Principle. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.36p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />37.
According to the mathematician Hermann Schwarz, there is one triangle
that can be inscribed within an acute triangle such that it has a
minimal perimeter. Using two planar mirrors, a laserbeam, and Fermat's
Principle, explain how you can show that this inscribed triangle has its
vertices at the points where the altitudes of the acute triangle
intersect its corresponding sides <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.37p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />38.
Show analytically that a beam entering a planar transparent plate, as
in Fig. P.4.34, emerges parallel to its initial direction. Derive an
expression for the lateral displacement of the beam. Incidentally, the
incoming and outgoing rays would be parallel even for a stack of plates
of different material.Figure P.4.34... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.38p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />39.
Show that the two rays that enter the system in Fig. P.4.35 parallel to
each other emerge from it being parallel.Figure. P.4.35... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.39p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />40.
Discuss the results of Problem 4.34 in the light of Fermat's Principle;
that is, how does the relative index n21 affect things? To see the
lateral displacement, look at a broad source through a thick piece of
glass (≈... inch) or a stack (four will do) of microscope slides held at
an angle. There will be an obvious shift between the region of the
source seen directly and the region viewed through the glass. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.40p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />41. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.41p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />42.
Suppose a lightwave that is linearly polarized in the
plane-of-incidence impinges at 30° on a crown-glass (ng = 1.52) plate in
air. Compute the appropriate amplitude reflection and transmission
coefficients at the interface. Compare your results with Fig. 4.39. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.42p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />43. Derive Eqs. (4.42) through (4.45) for r┴, r║, t┴, and r║. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.43p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />44.
A beam of light in air strikes the surface of a smooth piece of plastic
having an index of refraction of 1.55 at an angle with the normal of
20.0°. The incident light has component E-field amplitudes parallel and
perpendicular to the plane-of-incidence of 10.0 V/m and 20.0 V/m,
respectively. Determine the corresponding reflected field amplitudes. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.44p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />45.
A laserbeam is incident on the interface between air and some
dielectric of index n. For small values of θi- show that θt = θi/n. Use
this and Eq. (4.42) to establish that at near-normal incidence [-r┴]θi ≈
o = (n-1)/(n+ 1). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.45p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />46. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.46p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />47. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.47p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />48. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.48p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />49.
Light is incident in ah* perpendicularly on a sheet of crown glass
having an index of refraction of 1.522. Determine both the reflectance
and the transmittance. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.49p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />50.
A beam of quasimonochromalic light having an irradiance of 500 W/m2 is
incident in air perpendicularly on the surface of a tank of water (nw =
1.333). Determine the transmitted irradiance. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.50p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />51. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.51p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />52. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.52p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />53. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.53p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />55. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.55p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />56. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.56p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />57.
Quasimonochromatic light having an irradiance of 400 W/m2 is incident
normally on the cornea (nc = 1.376) of the human eye. If the person is
swimming under the water (nw = 1.33), determine the transmitted
irradiance into the cornea. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.57p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />58.
Compare the amplitude reflection coefficients for an air-water (nw =
4/3) interface with that of an air-crown glass (ng = 3/2) interface,
both at near-normal incidence. What are the corresponding ratios of the
reflected to the incident irradiances? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.58p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />59.
Use Eq. (4.42) and the power series expansion of the sine function to
establish that at near-normal incidence we can obtain a better
approximation than the one in Problem 4.41, which is [-r┴]θi ≈ o =
(n-1)/(n+ 1), namely... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.59p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />60.
Establish that at near-normal incidence the equation...is a good
approximation. [Hint: Use the results of the previous problem, Eq.
(4.43), and the power scries expansions of the sine and cosine
functions.] <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.60p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />61. Prove that for a vacuum-dielectric interface at glancing incidence r┴ → - 1, as in Fig. 4.41. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.61p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />62.
In Fig. 4.41 the curve of r┴ approaches -1.0 as the angle-of-incidence
approaches 90°. Prove that if α┴ is the angle the curve makes with the
vertical at θi-, = 90°, then...[Hint: First show that dθt/dθi = 0.] <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.62p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />63. Prove that...for all θt first from the boundary conditions and then from the Fresnel Equations. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.63p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />64. Verify that...for θi = 30° at a crown-glass and air interface (nti= 1.52). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.64p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />65. Use the Fresnel Equations to prove that light incident at θp ½π-θt results in a reflected beam that is indeed polarized. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.65p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />66.
Show that tan θp = nt/ni and calculate the polarization angle for
external incidence on a plate of crown glass (ng = 1.52) in air. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.66p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />67. Beginning with Eq. (4.38), show that for two dielectric media, in general tan ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.67p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />68.
Show that the polarization angles for internal and external reflection
at a given interface are complementary, that is, θp + θ’p = 90° (see
Problem 4.64). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.68p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />69.
It is often useful to work with the azimutkal angle γ, which isFigure
P.4.61 (Photo and diagram courtesy S. Reich, The Weizmann Institute of
Science, Israel....defined as the angle between the plane-of-vibration
and the plane-of-incidence. Thus for linearly polarized light,...Figure
P.4.67 is a plot of γr versus θi, for internal and external reflection
at an air-glass interface (nga = 1.51), where γt = 45°. Verify a few of
the points on the curves and in addition show that...Figure P.4.67... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.69p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />70. Making use of the definitions of the azimuthal angles in Problem 4.67, show that... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.70p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />71. Make a sketch of R┴ and R║ and nt = 1.5 and n, = 1 (i.e., internal reflection). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.71p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />72. Show that... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.72p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />73. Using the results of Problem 4.70, that is, Eqs. (4.98) and (4.99), show that...... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.73p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />74.
Suppose that we look at a source perpendicularly through a slack of N
microscope slides. The source seen through even a dozen slides will be
noticeably darker. Assuming negligible absorption, show that the total
iransmillance of the stack is given by...and evaluate Tt, for three
slides in air. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.74p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />75.
Making use of the expression...for an absorbing medium, we define a
quantity called the unit trans-mittance. T1. At normal incidence, Eq.
(4.55), T = It/Ii and thus when y = 1, T1 ≡ I(1)/Io. If the total
thickness of the slides in the previous problem is d and if they now
have a transmittanee per unit length T1, show that... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.75p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />76.
Show that at normal incidence on the boundary between two dielectrics,
as ... Moreover, prove that as nti ... Thus as the two media take on
more similar indices of refraction, less and less energy is carried off
in the reflected wave. It should be obvious that when nti = 1 there will
be no interface and no reflection. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.76p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />77. Derive the expressions for r┴ and r║ given by Eqs. (4.70) and (4.71). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.77p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />78. Show that when θi>θe at a dielectric interface, r┴ and r║ are complex and ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.78p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />79.
Calculate the critical angle beyond which there is total internal
reflection at an air-glass (ng = 1.5) interface. Compare this result
with that of Problem 4.15. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.79p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />80. Referring back to Problem 4.18, note that as θi,. increases θt increases. Prove that the maximum value θt ( may have is θc. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.80p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />81.
What is the critical angle for total internal reflection for diamond?
What, if anything, does the critical angle have to do with the luster of
a well-cut diamond? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.81p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />82.
Using a block of a transparent, unknown material, it is found that a
beam of light inside the material is totally internally reflected at the
air-block interface at an angle of 48.0°. What is its index of
refraetion? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.82p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />83.
A prism, ABC, is configured such that angle BCA = 90° and angle CBA =
45°. What is the minimum value of its index of refraction if, while
immersed in air, a beam traversing face AC is to be totally internally
reflected from face BC. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.83p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />84.
A fish looking straight up toward the smooth surface of a pond receives
a cone of rays and sees a circle of light filled with the images of sky
and birds and whatever else is up there. This bright circular field is
surrounded by darkness. Explain what is happening and compute the
cone-angle. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.84p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />85.
A glass block having an index of 1.55 is covered with a layer of water
of index 1.33. For light traveling in the glass, what is the critical
angle at the interface? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.85p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />86.
Derive an expression for the speed of the evanescent wave in the case
of internal reflection. Write it in terms of c, ni and θt <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.86p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />87.
Light having a vacuum wavelength of 600 nm, traveling in a...glass (ng =
1.50) block, is incident at 45° on a glass-air interface. It is then
totally internally reflected. Determine the distance into the air at
which the amplitude of the evanescent wave has dropped to a value of 1/e
of its maximum value at the interface. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.87p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />88. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.88p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />89. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.89p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />90. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.90p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />91.
Figure P.4.61 shows a laserbeam incident on a wet piece of filter paper
atop a sheet of glass whose index of refraction is to be measured—the
photograph shows the resulting light pattern. Explain what is happening
and derive an expression for ni in terms of R and d. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.91p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />92.
Consider the common mirage associated with an inhomoge-neous
distribution of air situated above a warm roadway. Envision the bending
of the rays as if it were instead a problem in total intet
nal-reflection. If an observer, at whose head na = 1.000 29, sees an
apparent wet spot at θi,≥ 88.7° down the road, find the index of the air
immediately above the road. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.92p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />93.
Figure P.4.80 depicts a glass cube surrounded by four glass prisms in
very close proximity to its sides. Sketch in the paths that will be
taken by the two rays shown and discuss a possible application for the
device.Figure P.4.80... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.93p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />94.
Figure P.4.82 shows a prism-coupler arrangement developed al the Bell
Telephone Laboratories. Its function is to feed a laserbeam into a thin
(0.00001-inch) transparent film, which then serves as a sort of
waveguide. One application is that of thin-film laserbeam circuitry—a
kind of integrated optics. How do you think it works?Figure P.4.82... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.94p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />95.
Figure P.4.81 is a plot of nt and nR versus A for a common am al.
Identify the metal by comparing its characteristics with those con
sidered in the chapter and discuss its optical properties.Figure
P.4.81... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.95p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />96. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.96p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />97. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.97p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />98. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.98p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />99.
Figure P.4.77 depicts a ray being multiply reflected by a transparent
dielectric plate (the amplitudes of the resulting fragments arc
indicated). As in Section 4.5, we use the primed coefficient notation
because the angles are related by Snell's Law.(a) Finish labeling the
amplitudes of the last four rays.(b) Show, using the Fresnel Equations,
that... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.99p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />100.
A wave, linearly polarized in the plane-of-incidence, impinges on the
interface between two dielectric media. If ... there is no reflected
wave, that is, ... Using Stokes's techFigure P.4.77...nique, start from
scratch to show that ... and θt = θp (Problem 4.66). How docs this
compare with Eq. (4.100)? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.100p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />101. Making use of the Fresnel Equations, show that ...as in the previous problem. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=4.101p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-78437641557177784872020-07-03T13:47:00.003-07:002020-07-03T13:47:59.658-07:00Chapter #3 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. Consider the plane electromagnetic wave (in SI units) given by
the expressions Ex = 0, Ey = 2 COS[2π × 1014(t - x/c) + π/2], and Ez =
0.(a) What are the frequency, wavelength, direction of motion,
amplitude, initial phase angle, and polarization of the wave?(b) Write
an expression for the magnetic flux density. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2.
Write an expression for the ... - and ... - fields that constitute a
plane harmonic wave traveling in the + z-direction. The wave is linearly
polarized with its plane of vibration at 45° to the yz-plane. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3.
Considering Eq. (3.3(1), show that the expression...is correct as it
applies to a plane wave for which the direction of the electric field is
constant. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4.
Imagine an electromagnetic wave with its E-field in the y-direction.
Show that Eq. (3.27)...applied to the harmonic wave ......yields the
fact thatE0 = CB0in agreement with Eq. (3.30). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5.
An electromagnetic wave is specified (in SI units) by the following
function:...Find (a) the direction along which the electric field
oscillates, (b) the scalar value of amplitude of the electric field, (c)
the direction of propagation of the wave, (d) the propagation number
and wavelength, (e) the frequency and angular frequency, and (f) the
speed. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6.
The electric field of an electromagnetic wave traveling in thepositive
.v-direction is given by...(a) Describe the field verbally, (b)
Determine an expression for k. (c) Find the phase speed of the wave. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8.
A 550-nm harmonic EM-wave whose electric field is in the z-direction is
traveling in the y-direction in vacuum, (a) What is the frequency of
the wave? (b) Determine both ω and k for this wave, (c) If the electric
field amplitude is 600 V/m, what is the amplitude of"the magnetic field?
(d) Write an expression for both E(t) and B(t) given that each is zero
at x = 0 and t = 0. Put in all the appropriate units. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13.
Calculate the energy input necessary to charge a parallel plate
capacitor by carrying charge from one plate to the other. Assume the
energy is stored in the field between the plates and compute the energy
per unit volume, uE, of that region, that is, Eq. (3.31). Hint: since
the electric field increases throughout the process, either integrate or
use its average value E/2. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14.
Starting with Eq. (3.32), prove that the energy densities of the
electric and magnet fields are equal (uE = uB) for an electromagnetic
wave. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15.
The time average of some function f(t) taken over an interval T is
given by...where t' is just a dummy variable. If T = 2π/ω is the period
of a harmonic function, show that ......when T = T and when T >>
T. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16. Show that a more general formulation of the previous problem yields ...for any interval T. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17. With the previous problem in mind, prove that...for any interval T. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18.
Prove that the irradiance of a harmonic EM-wave is given by...and then
determine the average rale at which energy is transported per unit area
by a plane wave having an amplitude of 15.0 V/m. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22.
A light bulb puts out 20 W of radiant energy (most of it IR). Assume it
to be a point source and calculate the irradiance 1.00 m away <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23.
Consider a linearly polarized plane electromagnetic wave traveling in
the +.x-direction in free space having as its plane of vibration the
.xy-plane. Given that ils frequency is 10 MHz and its amplitude is E0 =
0.08 V/m,(a) Find the period and wavelength of the wave.(b) Write an
expression for E(t) and B(t).(c) Find the flux density, (S), of the
wave. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24.
On average, the net electromagnetic power radiated by the Sun, its
so-called luminosity (L), is 3.9 X 1026 W. Determine the mean amplitude
of the electric field due to all the radiant energy arriving at the top
of Earth's atmosphere (1.5 X 1011m from the Sun). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25.
A linearly polarized, harmonic plane wave with a scalar amplitude of 10
V/m is propagating along a line in the xy -plane at 45° to the x-axis
with the ,xy-plane as its plane of vibration. Please write a vector
expression describing the wave assuming both kx and ky are positive.
Calculate the flux density taking the wave to be in vacuum. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26.
Pulses of UV lasting 2.00 ns each are emitted from a laser that has a
beam of diameter 2.5 mm. Given that each burst carries an energy of 6.0
J, (a) determine the length in space of each wavetrain, and (b) find the
average energy per unit volume for such a pulse. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27.
A laser provides pulses of EM-radiation in vacuum lasting 10-12 s. If
the radiant flux density is 1020 w/m2, determine the amplitude of the
electric field of the beam. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28.
A 1.0-mW laser has a beam diameter of 2 mm. Assuming the divergence of
the beam to be negligible, compute its energy density in the vicinity of
the laser. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29.
A cloud of locusts having a density of 100 insects per cubic meter is
flying north at a rate of 6 m/min. What is the flux density of locusts?
That is, how many cross an area of 1 m2 perpendicular to their flight
path per second? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30.
Imagine that you are standing in the path of an antenna that is
radiating plane waves of frequency 100 MHz and flux density 19,88 × 10-2
W/m2. Compute the photon flux density, that is, the number of photons
per unit time per unit area. How many photons, on the average, will be
found in a cubic meter of this region? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31.
How many photons per second are emitted from a 100-W yellow light bulb
if we assume negligible thermal losses and a quasi-monochromatic
wavelength of 550 nm? In actuality only about 2.5% of the total
dissipated power emerges as visible radiation in an ordinary 100-W lamp.
<a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32.
A 3.0-V flashlight bulb draws 0.25 A, converting about 1.0% of the
dissipated power into light (λ ≈ 550 nm). If the beam has a
cross-sectional area of 10cm2 and is approximately cylindrical,(a) How
many photons are emitted per second?(b) How many photons occupy each
meter of the beam?(c) What is the flux density of the beam as it leaves
the flashlight? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33.
An isotropic quasimonochromatic point source radiates at a rate of 100
W. What is the flux density at a distance of 1 m? What are the
amplitudes of the E- and B-fields at that point? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34.
Using energy arguments, show that the amplitude of a cylindrical wave
must vary inversely with .... Draw a diagram indicating what's
happening. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />35. What is the momentum of a 1019-Hz X-ray photon? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.35p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />36.
Consider an electromagnetic wave impinging on an electron. It is easy
to show kinematic-ally that the average value of the time rate-of-change
of the electron's momentum ... is proportional to the average value of
the time rate-of-change of the work, W, done on it by the wave. In
particular,...Accordingly, if this momentum change is imparted to some
completely absorbing material, show that the pressure is given by Eq.
(3.51). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.36p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />37. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.37p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />38.
Derive an expression for (he radiation pressure when the normally
incident beam of light is totally reflected. Generalize this result to
the case of oblique incidence at an angle θ with the normal. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.38p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />39.
A completely absorbing screen receives 300 W of light for 100 s.
Compute the total linear momentum transferred to the screen. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.39p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />40.
The average magnitude of the Poynting vector for sunlight arriving at
the top of Earth's atmosphere (1.5 X 1011 m from the Sun) is about 1.4
kW/m2.(a) Compute the average radiation pressure exerted on a metal
reflector facing the Sun.(b) Approximate the average radiation pressure
at the surface of the Sun whose diameter is 1.4 × 109m. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.40p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />41.
A surface is placed perpendicular to a beam of light of constant
irradiance (I). Suppose that the fraction of the irradiance absorbed by
the surface is a. Show that the pressure on the surface is given by... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.41p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />42.
A light beam with an irradiance of 2.00 × 106 W/m2 impinges normally on
a surface that reflects 70.0% and absorbs 30.0%. Compute the resulting
radiation pressure on the surface. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.42p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />43.
What force on the average will be exerted on the (40m × 50m) flat,
highly reflecting side of a space station wall if it's facing the Sun
while orbiting Earth?. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.43p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />44.
A parabolic radar antenna with a 2-m diameter transmits 200-kW pulses
of energy. If its repetition rate is 500 pulses per second, each lasting
2 µS, determine the average reaction force on the antenna. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.44p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />45.
Consider the plight of an astronaut floating in free space with only a
10-W lantern (inexhaustibly supplied with power). How long will it take
to reach a speed of 10 m/s using the radiation as propulsion? The
astronaut's total mass is 100 kg. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.45p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />46.
Consider the uniformly moving charge depicted in Fig. 3.266. Draw a
sphere surrounding it and show via the Poynting vector that the charge
does not radiate. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.46p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />47.
A plane, harmonic, linearly polarized light wave has an electric field
intensity given by...while traveling in a piece of glass. Find(a) The
frequency of the light.(b) Its wavelength.(c) The index of refraction of
the glass. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.47p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />48. What is the speed of light in diamond if the index of refraction is 2.42? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.48p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />49. Given that the wavelength of a light wave in vacuum is 540 nm, what will it be in water, where n = 1.33? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.49p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />50.
Determine the index of refraction of a medium if it is to reduce the
speed of light by 10% as compared to its speed in vacuum? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.50p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />51. If the speed of light (the phase speed) in Fabulite (SrTi03) is 1.245 × 108m/s, what is its index of refraction? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.51p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />52. What is the distance that yellow light travels in water (where n = 1.33) in 1.00 s? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.52p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />53.
A 500-nm lightwave in vacuum enters a glass plate of index 1.60 and
propagates perpendicularly across it. How many waves span the glass if
it's 1.00 cm thick? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.53p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />54.
Yellow light from a sodium lamp (λ0 = 589 nm) traverses a tank of
glycerin (of index 1.47), which is 20.0 m long, in a time t1. If it
takes a time t2 for the tight to pass through the same lank when filled
with carbon disulfide (of index 1.63), determine the value of t2-t1. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.54p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />55.
A lightwave travels from point A to point B in vacuum. Suppose we
introduce into its path a flat glass plate (ng = 1.50) of thickness L =
1.00 mm. If the vacuum wavelength is 500 nm, how many waves span the
space from A to B with and without the glass in place? What phase shift
is introduced with the insertion of the plate? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.55p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />56.
The low-frequency relative permittivity of water varies from 88.00 at
0°C to 55.33 at 100°C. Explain this behavior. Over the same range in
temperature, the index of refraction (λ = 589.3 nm) goes from roughly
1.33 to 1.32. Why is the change in n so much smaller than the
corresponding change in KE? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.56p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />57.
Show that for substances of low density, such as gases, which have a
single resonant frequency ω0, the index of refraction is given by... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.57p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />58.
In the next chapter, Eq. (4.47), we'll see that a substance reflects
radiant energy appreciably when its index differs most from the medium
in which it is embedded.(a) The dielectric constant of ice measured at
microwave frequencies is roughly 1, whereas that for water is about 80
times greater-why?(b) How is it that a radar beam easily passes through
ice but is considerably reflected when encountering a dense rain? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.58p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />59.
Fuchsin is a strong (aniline) dye, which in solution with alcohol has a
deep red color. It appears red because it absorbs the green component
of the spectrum. (As you might expect, the surfaces of crystals of
fuchsin reflect green light rather strongly.) Imagine that you have a
thin-walled hollow prism tilled with this solution. What will the
spectrum look like for incident white light? By the way, anomalous
dispersion was first observed in about 1840 by Fox Talbot, and the
effect was christened in 1862 by Le Roux. His work was promptly
forgotten, only to be rediscovered eight years later by C. Christiansen.
<a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.59p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />60. Take Eq. (3.71) and check out the units to make sure that they agree on both sides. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.60p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />61.
The resonant frequency of lead glass is in the UV fairly near the
visible, whereas that for fused silica is far into the UV. Use the
dispersion equation to make a rough sketch of n versus ω for the visible
region of the spectrum. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.61p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />62. Show that Eq. (3.70) can be rewritten as(n2 - 1)-1 = -Cλ-2 + Cλ0-2where C = 4π2c2ε0me/Nq2e <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.62p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />63.
Augustin Louis Cauchy (1789-1857) determined an empirical equation for
n(λ) for substances that are transparent in the visible. His expression
corresponded to the power series relationn = C1 + C2/λ2 + C3/λ4 +
•••where the Cs are all constants. In light of Fig. 3.41, what is the
physical significance of C1? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.63p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />64.
Referring to the previous problem, realize that there is a region
between each pair of absorption bands for which the Cauchy Equation
(with a new set of constants) works fairly well. Examine Fig. 3.41: what
can you say about the various values of C1 as ω decreases across the
spectrum? Dropping all but the first two terms, use Fig. 3.40 to
determine approximate values for C1 and C2 for borosilieate crown glass
in the visible. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.64p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />65.
Crystal quartz has refractive indexes of 1.557 and 1.547 at wavelengths
of 410.0 nm and 550.0 nm, respectively. Using only the first two terms
in Cauchy's Equation, calculate C1 and C2 and determine the index of
refraction of quartz at 610.0nm. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.65p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />66.
In 1871 Sellmeier derived the equation...where the Aj terms are
constants and each λoj is the vacuum wave- • length associated with a
natural frequence voj, such that λojvoj = c. This formulation is a
considerable practical improvement over the Cauchy Equation. Show that
where λ >> λoj, Cauchy's Equation is an approximation of
Sellmeier's. Hint: Write the above expression with only the first term
in the sum; expand it by the binomial theorem; lake the square root of
n2 and expand again. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.66p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />67.
If an ultraviolet photon is to dissociate the oxygen and carbon atoms
in the carbon monoxide molecule, it must provide 11 eV of energy. What
is the minimum frequency of the appropriate radiation? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=3.67p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.comtag:blogger.com,1999:blog-4876476322431362431.post-59876563512363906692020-07-03T13:47:00.001-07:002020-07-03T13:47:47.491-07:00Chapter #2 Solutions - Optics - Eugene Hecht - 5th Edition <div id="selectable2">
1. How many "yellow" lightwaves (λ = 580 nm) will fit into a
distance in space equal to the thickness of a piece of paper (0.003
in.)? How far will the same number of microwaves (v = 1010 Hz, i.e., 10
GHz, and v = 3 × 108 m/s) extend? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.1p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />2. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.2p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />3. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.3p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />4. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.4p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />5. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.5p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />6.
How many "yellow" lightwaves (λ = 580 nm) will fit into a distance in
space equal to the thickness of a piece of paper (0.003 in.)? How far
will the same number of microwaves (v = 1010 Hz, i.e., 10 GHz, and v = 3
× 108 m/s) extend? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.6p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />7.
The speed of light in vacuum is approximately 3 × 108 m/s. Find the
wavelength of red light having a frequency of 5 × 1014 Hz. Compare this
with the wavelength of a 60-Hz electromagnetic wave. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.7p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />8.
It is possible to generate ultrasonic waves in crystals with
wavelengths similar to light (5 × 10-5 cm) but with lower frequencies (6
× 108 Hz). Compute the corresponding speed of such a wave. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.8p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />9.
A youngster in a boat on a lake watches waves that seem to be an
endless succession of identical crests passing with a half-second
interval between each. If every disturbance takes 1.5 s to sweep
straight along the length of her 4.5-m-long boat, what are the
frequency, period, and wavelength of the waves? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.9p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />10.
A vibrating hammer strikes the end of a long metal rod in such a way
that a periodic compression wave with a wavelength of 4.3 m travels down
the rod's length at a speed of 3.5 km/s. What was the frequency of the
vibration? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.10p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />11.
A violin is submerged in a swimming pool at the wedding of two scuba
divers. Given that the speed of compression waves in pure water is 1498
m/s, what is the wavelength of an A-note of 440 Hz played on the
instrument? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.11p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />12.
A wavepulse travels 10 m along the length of a string in 2.0 s. A
harmonic disturbance of wavelength 0.50 m is then generated on the
string. What is its frequency? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.12p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />13. Show that for a periodic wave to = (2п/λ)v. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.13p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />14.
Make up a table with columns headed by values of θ running from - п/2
to 2 п in intervals of п /4. In each column place the corresponding
value of sin θ, beneath those the values of cos θ, beneath those the
values of sin (θ - п /4), and similarly with the functions sin (θ -
п/2), sin (θ - 3 п/4), and sin (θ + п/2). Plot each of these functions,
noting the effect of the phase shift. Docs sin θ lead or lag sin (θ -
п/2). In other words, does one of the functions reach a particular
magnitude at a smaller value of θ than the other and therefore lead the
other (as cos θ leads sin θ)? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.14p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />15.
Make up a table with columns headed by values of kx running from x =
-λ/2 to x = +λ in intervals of x of λ/4—of course, k = 2п/λ. In each
column place the corresponding values of cos (kx -п/4) and beneath that
the values of cos (kx + 3 п/4). Next plot the functions 15 cos (kx -
п/4) and 25 cos (kx + 3 п/4). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.15p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />16.
Make up a table with columns headed by values of ωt running from t =
-τ/2 to t = +τ in intervals of t. of τ/4-of course, ω = 2п/τ. In each
column place the corresponding values of sin ωt + п/4) and sin (п/4 - ωt
and then plot these two functions. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.16p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />17.
The profile of a transverse harmonic wave, traveling at 1.2 m/s on a
string, is given byy = (0.02 m) sin (157 m-1)xDetermine its amplitude,
wavelength, frequency, and period. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.17p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />18.
Figure P.2.13 represents the profile (t = 0) of a transverse wave on a
string traveling in the positive x-direction at a speed of, 20.0 m/s.
(a) Determine its wavelength, (b) What is the frequency of the wave? (c)
Write down the wavefunction for the disturbance, (d) Notice that as the
wave passes any fixed point on the. x-axis the string at that location
oscillates in time. Draw a graph of the ψ versus t showing how a point
on the rope at x = 0 oscillates.Figure P.2.13 ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.18p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />19.
Figure P.2.14 represents the profile (t = 0) of a transverse wave on a
string traveling in (he positive z-direction at a speed of 100 cm/s. (a)
Determine its wavelength, (b) Notice that as the wave passes any fixed
point on the z-axis the string at that location oscillates in time. Draw
a graph of the ψ versus t showing how a point on the rope at x = 0
oscillates, (c) What is the frequency of the wave? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.19p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />20.
A transverse wave on a string travels in the negative y-direction at a
speed of 40.0 cm/s. Figure P.2.15 is a graph of ψ versus t showing how a
point on the rope at y = 0 oscillates, (a) Determine the wave's period,
(b) What is the frequency of the wave? (b) What is the wavelength of
the wave? (d) Sketch the profile of the wave ((ψ versus y).Figure
P.2.15... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.20p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />21.
Given the wavefunctions...determine in each case the values of (a)
frequency, (b) wavelength, (e) period, (d) amplitude, (e) phase
velocity, and (f) direction of motion. Time is in seconds and x is in
meters <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.21p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />22.
The wavefunction of a transverse wave on a string isΨ(x, t) = (30.0 cm)
cos [(6.28 rad/m)x - (20.0 rad/s)t]Compute the (a) frequency, (b)
wavelength, (c) period, (d) amplitude, (e) phase velocity, and (f)
direction of motion. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.22p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />23. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.23p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />24. Show thatψ(x, t) = A sin k(x - vt)is a solution of the differential wave equation. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.24p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />25. Show thatψ(x, t) = A cos (kx – ωt)is a solution of the differential wave equation. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.25p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />26. Prove thatψ(x, t) = A sin (kx – ωt-п/2)is equivalent toψ(x, t) = A sin (kx – ωt) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.26p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />27.
Show that if the displacement of the string in Fig. 2.7 is given byy(x,
t) = A sin [kx – ωt+ ε]then the hand generating the wave must be moving
vertically in simple harmonic motion. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.27p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />28.
Write the expression for the wavefunction of a harmonic wave of
amplitude 103 V/m, period 2.2 × 10-15 s, and speed 3 × 108m/s. The wave
is propagating in the negative x-direction and has a value of 103 V/m at
t = 0 and x = 0. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.28p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />29.
Consider the pulse described in terms of its displacement at t = 0
by...where C is a constant. Draw the wave profile. Write an expression
for the wave, having a speed v in the negative as x-direction, as a
function of time t. If v = 1 m/s, sketch the profile at t = 2 s. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.29p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />30.
Please determine the magnitude of the wavefunction ψ(z, t) = A cos [k(z
+ vt) + п] at the point z = 0, when t = τ/2 and when t = 3τ/4. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.30p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />31. Does the following function, in which A is a constant,Ψ(y,t)0 = (y - vt)Arepresent a wave? Explain your reasoning. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.31p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />32. Use Eq. (2.33) to calculate the speed of the wave whose representation in SI units isΨ(y,t) = A cos п(3 X 106y + 9 × 1014t) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.32p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />33. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.33p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />34. Beginning with the following theorem: If z = f(x, y) and x = g(t),y = h(t), then...Derive Eq. (2.34). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.34p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />35.
Using the results of the previous problem, show that for a harmonic
wave with a phase Ф(x, t) = k(x - vt) we can determine the speed by
setting dФ/dt = 0. Apply the technique to Problem 2.26 to find the speed
of that wave. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.35p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />36.
A Gaussian wave has the form ψ(x, t) = Ae-a(bx+ct)2. Use the fact that
ψ(x, t) = f(x ± vt) to determine its speed and then verify your answer
using Eq. (2.34). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.36p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />37.
Create an expression for the profile of a harmonic wave traveling in
the z-direction whose magnitude at z = -λ/12 is 0.866, at z = +λ/6 is
1/2, and at z = λ/4 is 0. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.37p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />38.
Which of the following expressions correspond to traveling waves? For
each of those, what is the speed of the wave? The quantities a, b, and c
are positive constants.... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.38p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />39.
Determine which of the following describe traveling waves:...Where
appropriate, draw the profile and find the speed and direction of
motion. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.39p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />40.
Given the traveling wave ψ(x, t) = 5.0 exp (-ax2 - br2 - 2√abxt),
determine its direction of propagation. Calculate a few values of ψ and
make a sketch of the wave at t = 0, taking a = 25 m-2 and b = 9.0 s-2.
What is the speed of the wave? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.40p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />41.
Imagine a sound wave with a frequency of 1.10 kHz propagating with a
speed of 330 m/s. Determine the phase difference in radians between any
two points on the wave separated by 10.0 cm. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.41p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />42.
Consider a lightwave having a phase velocity of 3 × 108 m/s and a
frequency of 6 × 1014 Hz. What is the shortest distance along the wave
between any two points that have a phase difference of 30º? What phase
shift occurs at a given point in 10-6 s, and how many waves have passed
by in that lime? <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.42p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />43.
Write an expression for the wave shown in Fig. P.2.36. Find its
wavelength, velocity, frequency, and period.Figure P.2.36 A harmonic
wave.... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.43p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />44.
Working with exponentials directly, show that the magnitude of ψ =
Aeiωt is A. Then rederivc the same result using Euler's formula. Prove
that eiαeiβ = ei(α+β) <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.44p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />45. Show that the imaginary part of a complex number ... is given by ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.45p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />46. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.46p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />47. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.47p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />48. Beginning with Eq. (2.51), verify that...and that α2 + β2 + γ2 = 1Draw a sketch showing all the pertinent quantities. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.48p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />49.
Show that Eqs. (2.64) and (2.65), which are plane waves of arbitrary
form, satisfy the three-dimensional differential wave equation. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.49p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />50. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.50p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />51. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.51p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />52.
De BrOglie's hypothesis states that every particle has associated with
it a wavelength given by Planck's constant (h = 6.6 × 10-34 j.s) divided
by the particle's momentum. Compare the wavelength of a 6.0-kg stone
moving at a speed of 1.0 m/s with that of light. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.52p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />53.
Write an expression in Cartesian coordinates for a harmonic plane wave
of amplitude A and frequency ω propagating in the direction of the
vector k, which in tum lies on a line drawn from the origin to the point
(4, 2, I). Hint; First determine k and then dot it with ... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.53p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />54.
Write an expression in Cartesian coordinates for a harmonic plane wave
of amplitude A and frequency ω propagating in the positive x-direelion. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.54p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />55.
Show that ω(... may represent a plane wave where ... is normal to the
wavefront. Hint: Let ..., and ... be position vectors drawn to any two
points on the plane and show that .... <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.55p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />56. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.56p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />57.
Make up a table with columns headed by values of θ running from -п/2 to
2п in intervals of п/4. In each column place the corresponding value of
sin θ, and beneath those the values of 2 sin θ. Next add these, column
by column, to yield the corresponding values of the function sin θ + 2
sin θ. Plot each of these three functions, noting their relative
amplitudes and phases. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.57p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />58.
Make up a table with columns headed by values of θ running from - п/2
to 2п in intervals of п/4. In each column place the corresponding value
of sin θ, and beneath those the values of sin (θ - п/2). Next add these,
column by column, to yield the corresponding values of the function sin
θ + sin (θ - п/2). Plot each of these three functions, noting their
relative amplitudes and phases. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.58p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />59.
With the last two problems in mind, draw a plot of the three functions
(a) sin θ, (b) sin (θ - 3п/4), and (c) sin θ + sin (θ -3п/4). Compare
the amplitude of the combined function (c) in this case with that of the
previous problem. <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.59p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br />60.
Make up a table with columns headed by values of kx running from x =
-λ/2 to x = +λ in intervals of x of п/4. In each column place the
corresponding values of cos kx and beneath that the values of cos (kx +
п). Next plot the three functions cos kx, cos (kx + п), and cos kx + cos
(kx + п). <a href="https://www.vipserver.info/solutionsdt/excercise.asp?id=2.60p&idb=9780133977226" target="_blank" title="Solutions -Optics - - Eugene Hecht - (5th Edition) "> Get solution</a> <br /> <br /><br /></div>Book Solutionshttp://www.blogger.com/profile/03137910488530179659noreply@blogger.com