1. Get solution
2. Get solution
3. Get solution
4. Get solution
5. Get solution
6. Get solution
7. Get solution
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. Get solution
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 Get solution
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? Get solution
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? Get solution
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. Get solution
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... Get solution
14. Carry out the details leading to the expression for the visibility given by Eq. (12.22). Get solution
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... Get solution
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? Get solution
17. Get solution
18. Show that Eqs. (12.34) and (12.35) follow from Eqs. (12.32) and (12.33), Get solution
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. Get solution
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. Get solution
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. Get solution
22. Get solution
23. Get solution
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%? Get solution
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? Get solution
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... Get solution
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 Get solution
28. Get solution
29. Get solution
30. Get solution
2. Get solution
3. Get solution
4. Get solution
5. Get solution
6. Get solution
7. Get solution
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. Get solution
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 Get solution
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? Get solution
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? Get solution
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. Get solution
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... Get solution
14. Carry out the details leading to the expression for the visibility given by Eq. (12.22). Get solution
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... Get solution
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? Get solution
17. Get solution
18. Show that Eqs. (12.34) and (12.35) follow from Eqs. (12.32) and (12.33), Get solution
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. Get solution
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. Get solution
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. Get solution
22. Get solution
23. Get solution
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%? Get solution
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? Get solution
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... Get solution
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 Get solution
28. Get solution
29. Get solution
30. Get solution
