1. Work out the details leading to Eq. (6.8) Get solution
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. Get solution
3. Write an expression for the thickness d1 of a double-convex lens such that its focal length is infinite. Get solution
4. Get solution
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). Get solution
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. Get solution
7. Using Eq. (6.2), derive an expression for the focal length of a homogeneous transparent sphere of radius R. Locate its principal points. Get solution
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? Get solution
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. Get solution
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. Get solution
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. Get solution
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? Get solution
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? Get solution
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. Get solution
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. Get solution
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. Get solution
17. Get solution
18. Get solution
19. Get solution
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. Get solution
21. Prove that the determinant of the system matrix in Eq. (6.31) is equal to 1. Get solution
22. Establish that Eqs. (6.36) and (6.37) are equivalent to Eqs. (6.3) and (6.4), respectively. Get solution
23. Show that the planar surface of a concave-planar or convex-planar lens doesn' I contribute to the system matrix. Get solution
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. Get solution
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. Get solution
26. Get solution
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? Get solution
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. Get solution
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 Get solution
30. Referring back to Fig. 6.17A, show that when ... and ... all rays originating at P appear to come from P'. Get solution
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. Get solution
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 Get solution
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 Get solution
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). ... Get solution
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. Get solution
3. Write an expression for the thickness d1 of a double-convex lens such that its focal length is infinite. Get solution
4. Get solution
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). Get solution
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. Get solution
7. Using Eq. (6.2), derive an expression for the focal length of a homogeneous transparent sphere of radius R. Locate its principal points. Get solution
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? Get solution
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. Get solution
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. Get solution
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. Get solution
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? Get solution
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? Get solution
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. Get solution
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. Get solution
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. Get solution
17. Get solution
18. Get solution
19. Get solution
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. Get solution
21. Prove that the determinant of the system matrix in Eq. (6.31) is equal to 1. Get solution
22. Establish that Eqs. (6.36) and (6.37) are equivalent to Eqs. (6.3) and (6.4), respectively. Get solution
23. Show that the planar surface of a concave-planar or convex-planar lens doesn' I contribute to the system matrix. Get solution
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. Get solution
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. Get solution
26. Get solution
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? Get solution
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. Get solution
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 Get solution
30. Referring back to Fig. 6.17A, show that when ... and ... all rays originating at P appear to come from P'. Get solution
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. Get solution
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 Get solution
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 Get solution
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). ... Get solution
