1. Initially unpolarized light passes in turn through three linear
polarizers with transmission axes at 0°, 30°, and 60°, respectively,
relative to the horizontal. What is the irradiance of the product light,
expressed as a percentage of the unpolarized light irradiance? Get solution
2. At what angles will light, externally and internally reflected from a diamond-air interface, be completely linearly polarized? For diamond, n = 2.42. Get solution
3. Since a sheet of Polaroid is not an ideal polarizer, not all the energy of the ...-vibrations parallel to the TA are transmitted, nor are all ...-vibrations perpendicular to the TA absorbed. Suppose an energy fraction α is transmitted in the first case and a fraction β is transmitted in the second.a. Extend Malus’ law by calculating the irradiance transmitted by a pair of such polarizers with angle θ between their TAs. Assume initially unpolarized light of irradiance I0. Show that Malus’ law follows in the ideal case.b. Let α = 0.95 and β = 0.05 for a given sheet of Polaroid. Compare the irradiance with that of an ideal polarizer when unpolarized light is passed through two such sheets having a relative angle between TAs of 0°, 30°, 45°, and 90°.Figure 1.... Get solution
4. How thick should a half-wave plate of mica be in an application where laser light of 632.8 nm is being used? Appropriate refractive indices for mica are 1.599 and 1.594. Get solution
5. Describe what happens to unpolarized light incident on birefringent material when the OA is oriented as shown in each sketch in Figure 15-23. You will want to comment on the following considerations: Single or double refracted rays? Any phase retardation? Any polarization of refracted rays?e. Which orientation(s) would you use to make a quarter-wave plate?Figure 1. Parts (a)–(d).... Get solution
6. Consider a Soleil-Babinet compensator, as shown in Figure 15-11. Suppose the compensator is constructed of quartz and provides a maximum phase retardation of two full wavelengths of green mercury light (546.1 nm). Refractive indices of quartz at this wavelength are n∥ = 1.555 and n⊥ = 1.546.a. How does the total wedge thickness compare with that of the flat plate in the position of maximum retardation?b. How do they compare when the emergent light is circularly polarized? Get solution
7. A number of dichroic polarizers are available, each of which can be assumed perfect, that is, each passes 50% of the incident unpolarized light. Let the irradiance of the incident light on the first polarizer be I0.a. Using a sketch, show that if the polarizers have their transmission axes set at angle θ apart, the light transmitted by the pair is given by ...b. What percentage of the incident light energy is transmitted by the pair when their transmission axes are set at 0° and 90°, respectively?c. Five additional polarizers of this type are placed between the two just described, with their transmission axes set at 15°, 30°, 45°, 60°, and 75°, in that order, with the 15°-angle polarizer adjacent to the 0° polarizer, and so on. Now what percentage of the incident light energy is transmitted? Get solution
8. Vertically polarized light of irradiance I0 is incident on a series of N successive linear polarizers, each with its transmission axis offset from the previous one by a small angle θ. With the help of the Law of Malus, determine the value of N such that the final transmitted irradiance is IN = 0.9 I0 when the small angle offsets sum to 90°, that is when the initial vertical polarization is rotated to a horizontal polarization. Get solution
9. What minimum thickness should a piece of quartz have to act as a quarter-wave plate for a wavelength of 5893 Å in vacuum? Get solution
10. Determine the angle of deviation between the two emerging beams of a Wollaston prism constructed of calcite and with wedge angle of 45°. Assume sodium light.Figure 1.... Get solution
11. A beam of linearly polarized light is changed into circularly polarized light by passing it through a slice of crystal 0.003 cm thick. Calculate the difference in the refractive indices for the two rays in the crystal, assuming this to be the minimum thickness showing the effect for a wavelength of 600 nm. Sketch the arrangement, showing the OA of the crystal, and explain why this occurs. Get solution
12. Light is incident on a water surface at such an angle that the reflected light is completely linearly polarized.a. What is the angle of incidence?b. The light refracted into the water is intercepted by the top flat surface of a block of glass with index of 1.50. The light reflected from the glass is completely linearly polarized. What is the angle between the glass and water surfaces?Figure 1.... Get solution
13. In each of the following cases, deduce the nature of the light that is consistent with the analysis performed. Assume a 100% efficient polarizer.a. When a polarizer is rotated in the path of the light, there is no intensity variation. With a QWP in front of the rotating polarizer (coming first), one finds a variation in intensity but no angular position of the polarizer that gives zero intensity.b. When a polarizer is rotated in the path of the light, there is some intensity variation but no position of the polarizer giving zero intensity. The polarizer is set to give maximum intensity. A QWP is allowed to intercept the beam first with its OA parallel to the TA of the polarizer. Rotation of the polarizer now can produce zero intensity. Get solution
14. Light from a source immersed in oil of refractive index 1.62 is incident on the plane face of a diamond (n = 2.42), also immersed in the oil. Determine (a) the angle of incidence at which maximum polarization occurs and (b) the angle of refraction into the diamond. Get solution
15. The rotation of polarized light in an optically active medium is found to be approximately proportional to the inverse square of the wavelength.a. The specific rotation of glucose is 20.5°. A glucose solution of unknown concentration is contained in a 12-cm-long tube and is found to rotate linearly polarized light by 1.23°. What is the concentration of the solution?b. Upon passing through a 1-mm-thick quartz plate, red light is rotated about 15°. What rotation would you expect for violet light? Get solution
16. a. What thickness of quartz is required to give an optical rotation of 10° for light of 396.8 nm?b. What is the specific rotation of quartz for this wavelength? The refractive indices for quartz at this wavelength, for left- and right-circularly polarized light, are ... and ..., respectively. Get solution
17. a. A thin plate of calcite is cut with its OA parallel to the plane of the plate. What minimum thickness is required to produce a quarter-wave path difference for sodium light of 589 nm?b. What color will be transmitted by a zircon plate, 0.0182 mm thick, when placed in a 45° orientation between crossed polarizers? Get solution
18. a. Show that polarizing angles for internal and external reflection between the same two media must be complementary.b. Show that if Brewster’s angle is satisfied for a TM light beam entering a parallel plate (a Brewster window), it will also be satisfied for the beam as it leaves the plate on the opposite side. Get solution
19. The indices of refraction for the fast and slow axes of quartz with 546 nm light are 1.5462 and 1.5553, respectively.a. By what fraction of a wavelength is the e-ray retarded, relative to the o-ray, for every wavelength of travel in the quartz?b. What is the thickness of a zeroth-order QWP?c. If a multiple-order quartz plate 0.735 mm thick functions as a QWP, what is its order m?d. Two quartz plates are optically contacted so that they produce opposing retardations. Sketch the orientation of the OA of the two plates. What should their difference in thickness be such that they function together like a zeroth-order QWP? Get solution
20. When a plastic triangle is viewed between crossed polarizers and with monochromatic light of 500 nm, a series of alternating transmission and extinction bands is observed. How much does (n⊥ − n∥) vary between transmission bands to satisfy successive conditions for HWP retardation? The plastic triangle is .... thick. Get solution
21. A plane plate of beryl is cut with the optic axis in the plane of the surfaces. Linearly polarized light is incident on the plate such that the ...-field vibrations are at 45° to the optic axis. Determine the smallest thickness of the plate such that the emergent light is (a) linearly and (b) circularly polarized. Get solution
22. Find the angle at which a half-wave plate must be set to compensate for the rotation of a 1.15-mm levorotatory quartz plate using 546-nm wavelength light. Get solution
23. In Chapter 23, the Fresnel equations are derived, showing that the fraction r of the incident field that is reflected from a dielectric plane surface for the TE polarization mode is given by Eq. (23-27). Thus, the reflectance R = r2 has the form, ...where θ is the angle of incidence and n is the ratio n2/n1.a. Calculate the reflectance R for the TE mode when the light is incident from air onto glass of n = 1.50 at the polarizing angle.b. The reflectance calculated in part (a) is also valid for an internal reflection as light leaves the glass going into air. This being the case, calculate the net fraction of the TE mode transmitted through a stack of 10 such plates relative to the incident irradiance I0. Assume that the plates do not absorb light and that there are no multiple reflections within the plates.c. Calculate the degree of polarization P of the transmitted beam, given by ...where I stands for the irradiance of either polarization mode. Get solution
24. A half-wave plate is placed between crossed polarizer and analyzer such that the angle between the polarizer TA and the FA of the HWP is θ. How does the emergent light vary as a function of θ?Figure 1.... Get solution
25. a. Determine the rotation produced by the optical activity of a 3-mm quartz plate on a linearly polarized beam of light at wavelength 762 nm.b. What is the rotation clue to optical activity by a half-wave plate of quartz using the same light beam? Get solution
2. At what angles will light, externally and internally reflected from a diamond-air interface, be completely linearly polarized? For diamond, n = 2.42. Get solution
3. Since a sheet of Polaroid is not an ideal polarizer, not all the energy of the ...-vibrations parallel to the TA are transmitted, nor are all ...-vibrations perpendicular to the TA absorbed. Suppose an energy fraction α is transmitted in the first case and a fraction β is transmitted in the second.a. Extend Malus’ law by calculating the irradiance transmitted by a pair of such polarizers with angle θ between their TAs. Assume initially unpolarized light of irradiance I0. Show that Malus’ law follows in the ideal case.b. Let α = 0.95 and β = 0.05 for a given sheet of Polaroid. Compare the irradiance with that of an ideal polarizer when unpolarized light is passed through two such sheets having a relative angle between TAs of 0°, 30°, 45°, and 90°.Figure 1.... Get solution
4. How thick should a half-wave plate of mica be in an application where laser light of 632.8 nm is being used? Appropriate refractive indices for mica are 1.599 and 1.594. Get solution
5. Describe what happens to unpolarized light incident on birefringent material when the OA is oriented as shown in each sketch in Figure 15-23. You will want to comment on the following considerations: Single or double refracted rays? Any phase retardation? Any polarization of refracted rays?e. Which orientation(s) would you use to make a quarter-wave plate?Figure 1. Parts (a)–(d).... Get solution
6. Consider a Soleil-Babinet compensator, as shown in Figure 15-11. Suppose the compensator is constructed of quartz and provides a maximum phase retardation of two full wavelengths of green mercury light (546.1 nm). Refractive indices of quartz at this wavelength are n∥ = 1.555 and n⊥ = 1.546.a. How does the total wedge thickness compare with that of the flat plate in the position of maximum retardation?b. How do they compare when the emergent light is circularly polarized? Get solution
7. A number of dichroic polarizers are available, each of which can be assumed perfect, that is, each passes 50% of the incident unpolarized light. Let the irradiance of the incident light on the first polarizer be I0.a. Using a sketch, show that if the polarizers have their transmission axes set at angle θ apart, the light transmitted by the pair is given by ...b. What percentage of the incident light energy is transmitted by the pair when their transmission axes are set at 0° and 90°, respectively?c. Five additional polarizers of this type are placed between the two just described, with their transmission axes set at 15°, 30°, 45°, 60°, and 75°, in that order, with the 15°-angle polarizer adjacent to the 0° polarizer, and so on. Now what percentage of the incident light energy is transmitted? Get solution
8. Vertically polarized light of irradiance I0 is incident on a series of N successive linear polarizers, each with its transmission axis offset from the previous one by a small angle θ. With the help of the Law of Malus, determine the value of N such that the final transmitted irradiance is IN = 0.9 I0 when the small angle offsets sum to 90°, that is when the initial vertical polarization is rotated to a horizontal polarization. Get solution
9. What minimum thickness should a piece of quartz have to act as a quarter-wave plate for a wavelength of 5893 Å in vacuum? Get solution
10. Determine the angle of deviation between the two emerging beams of a Wollaston prism constructed of calcite and with wedge angle of 45°. Assume sodium light.Figure 1.... Get solution
11. A beam of linearly polarized light is changed into circularly polarized light by passing it through a slice of crystal 0.003 cm thick. Calculate the difference in the refractive indices for the two rays in the crystal, assuming this to be the minimum thickness showing the effect for a wavelength of 600 nm. Sketch the arrangement, showing the OA of the crystal, and explain why this occurs. Get solution
12. Light is incident on a water surface at such an angle that the reflected light is completely linearly polarized.a. What is the angle of incidence?b. The light refracted into the water is intercepted by the top flat surface of a block of glass with index of 1.50. The light reflected from the glass is completely linearly polarized. What is the angle between the glass and water surfaces?Figure 1.... Get solution
13. In each of the following cases, deduce the nature of the light that is consistent with the analysis performed. Assume a 100% efficient polarizer.a. When a polarizer is rotated in the path of the light, there is no intensity variation. With a QWP in front of the rotating polarizer (coming first), one finds a variation in intensity but no angular position of the polarizer that gives zero intensity.b. When a polarizer is rotated in the path of the light, there is some intensity variation but no position of the polarizer giving zero intensity. The polarizer is set to give maximum intensity. A QWP is allowed to intercept the beam first with its OA parallel to the TA of the polarizer. Rotation of the polarizer now can produce zero intensity. Get solution
14. Light from a source immersed in oil of refractive index 1.62 is incident on the plane face of a diamond (n = 2.42), also immersed in the oil. Determine (a) the angle of incidence at which maximum polarization occurs and (b) the angle of refraction into the diamond. Get solution
15. The rotation of polarized light in an optically active medium is found to be approximately proportional to the inverse square of the wavelength.a. The specific rotation of glucose is 20.5°. A glucose solution of unknown concentration is contained in a 12-cm-long tube and is found to rotate linearly polarized light by 1.23°. What is the concentration of the solution?b. Upon passing through a 1-mm-thick quartz plate, red light is rotated about 15°. What rotation would you expect for violet light? Get solution
16. a. What thickness of quartz is required to give an optical rotation of 10° for light of 396.8 nm?b. What is the specific rotation of quartz for this wavelength? The refractive indices for quartz at this wavelength, for left- and right-circularly polarized light, are ... and ..., respectively. Get solution
17. a. A thin plate of calcite is cut with its OA parallel to the plane of the plate. What minimum thickness is required to produce a quarter-wave path difference for sodium light of 589 nm?b. What color will be transmitted by a zircon plate, 0.0182 mm thick, when placed in a 45° orientation between crossed polarizers? Get solution
18. a. Show that polarizing angles for internal and external reflection between the same two media must be complementary.b. Show that if Brewster’s angle is satisfied for a TM light beam entering a parallel plate (a Brewster window), it will also be satisfied for the beam as it leaves the plate on the opposite side. Get solution
19. The indices of refraction for the fast and slow axes of quartz with 546 nm light are 1.5462 and 1.5553, respectively.a. By what fraction of a wavelength is the e-ray retarded, relative to the o-ray, for every wavelength of travel in the quartz?b. What is the thickness of a zeroth-order QWP?c. If a multiple-order quartz plate 0.735 mm thick functions as a QWP, what is its order m?d. Two quartz plates are optically contacted so that they produce opposing retardations. Sketch the orientation of the OA of the two plates. What should their difference in thickness be such that they function together like a zeroth-order QWP? Get solution
20. When a plastic triangle is viewed between crossed polarizers and with monochromatic light of 500 nm, a series of alternating transmission and extinction bands is observed. How much does (n⊥ − n∥) vary between transmission bands to satisfy successive conditions for HWP retardation? The plastic triangle is .... thick. Get solution
21. A plane plate of beryl is cut with the optic axis in the plane of the surfaces. Linearly polarized light is incident on the plate such that the ...-field vibrations are at 45° to the optic axis. Determine the smallest thickness of the plate such that the emergent light is (a) linearly and (b) circularly polarized. Get solution
22. Find the angle at which a half-wave plate must be set to compensate for the rotation of a 1.15-mm levorotatory quartz plate using 546-nm wavelength light. Get solution
23. In Chapter 23, the Fresnel equations are derived, showing that the fraction r of the incident field that is reflected from a dielectric plane surface for the TE polarization mode is given by Eq. (23-27). Thus, the reflectance R = r2 has the form, ...where θ is the angle of incidence and n is the ratio n2/n1.a. Calculate the reflectance R for the TE mode when the light is incident from air onto glass of n = 1.50 at the polarizing angle.b. The reflectance calculated in part (a) is also valid for an internal reflection as light leaves the glass going into air. This being the case, calculate the net fraction of the TE mode transmitted through a stack of 10 such plates relative to the incident irradiance I0. Assume that the plates do not absorb light and that there are no multiple reflections within the plates.c. Calculate the degree of polarization P of the transmitted beam, given by ...where I stands for the irradiance of either polarization mode. Get solution
24. A half-wave plate is placed between crossed polarizer and analyzer such that the angle between the polarizer TA and the FA of the HWP is θ. How does the emergent light vary as a function of θ?Figure 1.... Get solution
25. a. Determine the rotation produced by the optical activity of a 3-mm quartz plate on a linearly polarized beam of light at wavelength 762 nm.b. What is the rotation clue to optical activity by a half-wave plate of quartz using the same light beam? Get solution
No hay comentarios:
Publicar un comentario