1. Discuss the state of polarization when the x and y components of
the electric field are given by the following equations:(a) ...
(b) ...(c) ... (d) ... In each case, plot the rotation of the tip of
the electric vector on the plane z = 0.[Ans: (a) Linearly polarized, (b)
Right-circularly polarized, (c) Left-circularly polarized, and (d)
Left-elliptically polarized.] Get solution
2. The electric field components of a plane electromagnetic wave are Ex = 2E0 cos (ωt – kz + ϕ) ; Ey = E0 sin (ωt – kz)Draw the diagram showing the state of polarization (i.e., circular, plane, elliptical or unpolarized) when (a) ϕ = 0 (b) ϕ = π/2 (c) ϕ = π/4 Get solution
3. Using the data given in Table 22.1, calculate the thickness of quartz half wave plate for λ0 = 5890Å. [Ans: 32.34 μm] Get solution
4. A right-circularly polarized beam is incident on a calcite half-wave plate. Show that the emergent beam will be left-circularly polarized. Get solution
5. What will be the Brewster angle for a glass slab (n = 1.5) immersed in water (n = 4/3). [Ans: 48.4°] Get solution
6. Consider the normal incidence of a plane wave on a quartz quarter wave plate whose optic axis is parallel to the surface (see Fig. 22.24). Thus the optic axis is along the z-axis and the propagation is along the x-axis. Show that Ey propagates as an o-wave and Ez as an e-wave.(a) Assuming... at x = 0 show that the emergent light would be right circularly polarized.(b) On the other hand, if one assumes... at x = 0 show that the emergent beam is linearly polarized. Get solution
7. Show that the angle between the vectors D and E is the same as between the Poynting vector S and the propagation vector k. Get solution
8. Consider the propagation of an extra-ordinary wave through a KDP crystal. If the wave vector is at an angle of 45° to the optic axis, calculate the angle between S and k. Repeat the calculation for LiNbO3. The values of no and ne for KDP and LiNbO3 are given in Table 22.1. [Ans: 1.56° and 2.25°] Get solution
9. Prove that when the angle of incidence corresponds to the Brewster angle, the reflected and refracted rays are at right angles to each other. Get solution
10. (a) Consider two crossed polaroids placed in the path of an unpolarized beam of intensity I0 (see Fig. 22.6). If we place a third polaroid in between the two then, in general, some light will be transmitted through. Explain this phenomenon. (b) Assuming the pass axis of the third polaroid to be at 45° to the pass axis of either of the polaroids, calculate the intensity of the transmitted beam. Assume that all the polaroids are perfect. [Ans: 1/8 I0] Get solution
11. A quarter-wave plate is rotated between two crossed polaroids. If an unpolarized beam is incident on the first polaroid, discuss the variation of intensity of the emergent beam as the quarter-wave plate is rotated. What will happen if we have a half-wave instead of a quarter-wave plate? Get solution
12. In Problem 22.11, if the optic axis of the quarter-wave plate makes an angle of 45° with the pass axis of either polaroid, show that only a quarter of the incident intensity will be transmitted. If the quarter-wave plate is replaced by a half-wave plate, show that half of the incident intensity will be transmitted through. Get solution
13. ...For calcite, the values of no and ne for λ0 = 4046Å are 1.68134 and 1.49694 respectively; corresponding to λ0 = 7065Å the values are 1.65207 and 1.48359 respectively. We have a calcite quarter-wave plate corresponding to λ0 = 4046Å. A left-circularly polarized beam of λ0 = 7065Å is incident on this plate. Obtain the state of polarization of the emergent beam. Get solution
14. A HWP (half wave plate) is introduced between two crossed polaroids P1 and P2. The optic axis makes an angle 15° with the pass axis of P1 as shown in Fig. 22.39(a) and (b). If an unpolarized beam of intensity I0 is normally incident on P1 and if I1, I2, and I3 are the intensities after P1, after HWP and after P2 respectively then calculate I1/I0, I2/I0 and I3/I0.[Ans: ½, ½, ⅛] Get solution
15. Two prisms of calcite (no > ne) are cemented together as shown in Fig. 22.40, so as to form a cube. Lines and dots show the direction of the optic axis. A beam of unpolarized light is incident normally from region I. Assume the angle of the prism to be 12°. Determine the path of rays in regions II, III & IV indicating the direction of vibrations (i.e., the direction of ).... Get solution
16. A λ/6 plate is introduced in between the two crossed polarizers in such a way that the optic axis of the λ/6 plate makes an angle of 45° with the pass axis of the first polarizer (see Fig. 22.41). Consider an unpolarized beam of intensity I0 to be incident normally on the polarizer. Assume the optic axis to be along the z-axis and the propagation along the x-axis. Write the y and z components of the electric fields (and the corresponding total intensities) after passing through (i) P1 (ii) λ/6 plate and (iii) P2 .... Get solution
17. A beam of light is passed through a polarizer. If the polarizer is rotated with the beam as an axis, the intensity I of the emergent beam does not vary. What are the possible states of polarization of the incident beam? How to ascertain its state of polarization with the help of the given polarizer and a QWP? Get solution
18. Consider a Wollaston prism consisting of two similar prisms of calcite (no = 1.66 and ne = 1.49) as shown in Fig. 22.29, with angle of prism now equal to 25°. Calculate the angular divergence of the two emerging beams. Get solution
19. (a) Consider a plane wave incident normally on a calcite crystal with its optic axis making an angle of 20° with the normal [see Fig. 19.18(a)]. Thus ψ = 20°. Calculate the angle that the Poynting vector will make with the normal to the surface. Assume no ≈ 1.66 and ne ≈ 1.49. (b) In the above problem assume the crystal to be quartz with no ≈ 1.544 and ne ≈ 1.553. [Ans: (a) 4.31°] Get solution
20. Consider the incidence of he following REP beam on a sugar solution at z = 0:Ex = 5 cos ωt ; Ey = 4 sin ωt with λ = 6328Å. Assume nl – nr = 10 –5 and nl = 4/3 study the evolution of the SOP of the beam. Get solution
21. Consider the incidence of the above REP beam on an elliptic core fiber with ... 1.506845 and ... 1.507716 Calculate the SOP at z = 0.25 Lb, 0.5 Lb, 0.75 Lb and Lb. Get solution
22. When the optic axis lies on the surface of the crystal and in the plane of incidence, show (by geometrical considerations) that the angles of refraction of the ordinary and the extra-ordinary rays (which we denote by ro and re respectively) are related through the following equation: ... Get solution
11&12. Get solution
2. The electric field components of a plane electromagnetic wave are Ex = 2E0 cos (ωt – kz + ϕ) ; Ey = E0 sin (ωt – kz)Draw the diagram showing the state of polarization (i.e., circular, plane, elliptical or unpolarized) when (a) ϕ = 0 (b) ϕ = π/2 (c) ϕ = π/4 Get solution
3. Using the data given in Table 22.1, calculate the thickness of quartz half wave plate for λ0 = 5890Å. [Ans: 32.34 μm] Get solution
4. A right-circularly polarized beam is incident on a calcite half-wave plate. Show that the emergent beam will be left-circularly polarized. Get solution
5. What will be the Brewster angle for a glass slab (n = 1.5) immersed in water (n = 4/3). [Ans: 48.4°] Get solution
6. Consider the normal incidence of a plane wave on a quartz quarter wave plate whose optic axis is parallel to the surface (see Fig. 22.24). Thus the optic axis is along the z-axis and the propagation is along the x-axis. Show that Ey propagates as an o-wave and Ez as an e-wave.(a) Assuming... at x = 0 show that the emergent light would be right circularly polarized.(b) On the other hand, if one assumes... at x = 0 show that the emergent beam is linearly polarized. Get solution
7. Show that the angle between the vectors D and E is the same as between the Poynting vector S and the propagation vector k. Get solution
8. Consider the propagation of an extra-ordinary wave through a KDP crystal. If the wave vector is at an angle of 45° to the optic axis, calculate the angle between S and k. Repeat the calculation for LiNbO3. The values of no and ne for KDP and LiNbO3 are given in Table 22.1. [Ans: 1.56° and 2.25°] Get solution
9. Prove that when the angle of incidence corresponds to the Brewster angle, the reflected and refracted rays are at right angles to each other. Get solution
10. (a) Consider two crossed polaroids placed in the path of an unpolarized beam of intensity I0 (see Fig. 22.6). If we place a third polaroid in between the two then, in general, some light will be transmitted through. Explain this phenomenon. (b) Assuming the pass axis of the third polaroid to be at 45° to the pass axis of either of the polaroids, calculate the intensity of the transmitted beam. Assume that all the polaroids are perfect. [Ans: 1/8 I0] Get solution
11. A quarter-wave plate is rotated between two crossed polaroids. If an unpolarized beam is incident on the first polaroid, discuss the variation of intensity of the emergent beam as the quarter-wave plate is rotated. What will happen if we have a half-wave instead of a quarter-wave plate? Get solution
12. In Problem 22.11, if the optic axis of the quarter-wave plate makes an angle of 45° with the pass axis of either polaroid, show that only a quarter of the incident intensity will be transmitted. If the quarter-wave plate is replaced by a half-wave plate, show that half of the incident intensity will be transmitted through. Get solution
13. ...For calcite, the values of no and ne for λ0 = 4046Å are 1.68134 and 1.49694 respectively; corresponding to λ0 = 7065Å the values are 1.65207 and 1.48359 respectively. We have a calcite quarter-wave plate corresponding to λ0 = 4046Å. A left-circularly polarized beam of λ0 = 7065Å is incident on this plate. Obtain the state of polarization of the emergent beam. Get solution
14. A HWP (half wave plate) is introduced between two crossed polaroids P1 and P2. The optic axis makes an angle 15° with the pass axis of P1 as shown in Fig. 22.39(a) and (b). If an unpolarized beam of intensity I0 is normally incident on P1 and if I1, I2, and I3 are the intensities after P1, after HWP and after P2 respectively then calculate I1/I0, I2/I0 and I3/I0.[Ans: ½, ½, ⅛] Get solution
15. Two prisms of calcite (no > ne) are cemented together as shown in Fig. 22.40, so as to form a cube. Lines and dots show the direction of the optic axis. A beam of unpolarized light is incident normally from region I. Assume the angle of the prism to be 12°. Determine the path of rays in regions II, III & IV indicating the direction of vibrations (i.e., the direction of ).... Get solution
16. A λ/6 plate is introduced in between the two crossed polarizers in such a way that the optic axis of the λ/6 plate makes an angle of 45° with the pass axis of the first polarizer (see Fig. 22.41). Consider an unpolarized beam of intensity I0 to be incident normally on the polarizer. Assume the optic axis to be along the z-axis and the propagation along the x-axis. Write the y and z components of the electric fields (and the corresponding total intensities) after passing through (i) P1 (ii) λ/6 plate and (iii) P2 .... Get solution
17. A beam of light is passed through a polarizer. If the polarizer is rotated with the beam as an axis, the intensity I of the emergent beam does not vary. What are the possible states of polarization of the incident beam? How to ascertain its state of polarization with the help of the given polarizer and a QWP? Get solution
18. Consider a Wollaston prism consisting of two similar prisms of calcite (no = 1.66 and ne = 1.49) as shown in Fig. 22.29, with angle of prism now equal to 25°. Calculate the angular divergence of the two emerging beams. Get solution
19. (a) Consider a plane wave incident normally on a calcite crystal with its optic axis making an angle of 20° with the normal [see Fig. 19.18(a)]. Thus ψ = 20°. Calculate the angle that the Poynting vector will make with the normal to the surface. Assume no ≈ 1.66 and ne ≈ 1.49. (b) In the above problem assume the crystal to be quartz with no ≈ 1.544 and ne ≈ 1.553. [Ans: (a) 4.31°] Get solution
20. Consider the incidence of he following REP beam on a sugar solution at z = 0:Ex = 5 cos ωt ; Ey = 4 sin ωt with λ = 6328Å. Assume nl – nr = 10 –5 and nl = 4/3 study the evolution of the SOP of the beam. Get solution
21. Consider the incidence of the above REP beam on an elliptic core fiber with ... 1.506845 and ... 1.507716 Calculate the SOP at z = 0.25 Lb, 0.5 Lb, 0.75 Lb and Lb. Get solution
22. When the optic axis lies on the surface of the crystal and in the plane of incidence, show (by geometrical considerations) that the angles of refraction of the ordinary and the extra-ordinary rays (which we denote by ro and re respectively) are related through the following equation: ... Get solution
11&12. Get solution
