1. Show that the vanishing of the reflection coefficient in the TM
mode, Eq. (23-28), occurs at Brewster’s angle, θp = tan−1(n). Get solution
2. The critical angle for a certain oil is found to be 33°33′. What are its Brewster’s angles for both external and internal reflections? Get solution
3. Determine the critical angle and polarizing angles for (a) external and (b) internal reflections from dense flint glass of index n = 1.84. Get solution
4. For what refractive index are the critical angle and (external) Brewster angle equal when the first medium is air? Get solution
5. Show that the Fresnel equations, Eqs. (23-27) to (23-30), may also be expressed by ... Get solution
6. Show that Eq. (23-37) follows from Eq. (23-35). Get solution
7. Using Eqs. (23-27) through (23-30) and a computer program or a computer algebra system, reproduce Figures 23-3 and 23-5. Also, change the value of n to produce graphs for the case of external and internal reflection from diamond (n = 2.42). Get solution
8. Use a computer to calculate and plot the reflectance curves of Figure 23-4. Also plot the corresponding transmittance. Get solution
9. Use a computer to calculate and plot the phase shifts on reflection as a function of angle of incidence for θ > θc. Take n = 1/1.5 to reproduce Figure 23-6 and then make similar plots for n = 1/1.3 and n = 1/2.42. Get solution
10. A film of magnesium fluoride is deposited onto a glass substrate with optical thickness equal to one-fourth the wavelength of the light to be reflected from it. Refractive indices for the film and substrate are 1.38 and 1.52, respectively. Assume that the film is nonabsorbing. For monochromatic light incident normally on the film, determine (a) reflectance from the air–film surface; (b) reflectance from the film–glass surface; (c) reflectance from an air–glass surface without the film; (d) net reflectance from the combination. See Eq. (22-43). Get solution
11. Calculate the reflectance of water (n = 1.33) for both (a) TE and (b) TM polarizations when the angles of incidence are 0°, 10°, 45°, and 90°. Get solution
12. Light is incident upon an air–diamond interface. If the index of diamond is 2.42, calculate the Brewster and critical angles for both (a) external and (b) internal reflections. In each case distinguish between polarization modes. Get solution
13. Calculate the percent reflectance and transmittance for both (a) TE and (b) TM modes of light incident at 50° on a glass surface of index 1.60. Get solution
14. Derive Eqs. (23-29) and (23-30) for the transmission coefficients both by (a) eliminating Er from Eqs. (23-20) to (23-23) and by (b) using the corresponding equations for the reflection coefficients, together with the relationships between reflection and transmission coefficients implied by Eqs. (23-20) and (23-22). Get solution
15. Unpolarized light is reflected from a plane surface of fused silica glass of index 1.458.a. Determine the critical and polarizing angles.b. Determine the reflectance and transmittance for the TE mode at normal incidence and at 45°.c. Repeat (b) for the TM mode.d. Calculate the phase difference between TM and TE modes for internally reflected rays at angles of incidence of 0°, 20°, 40°, 50°, 70°, and 90°. Get solution
17. Determine the reflectance for metallic reflection of sodium light (589.3 nm) from steel, for which nR = 2.485 and nI = 1.381. Calculate reflectance for (a) TE and (b) TM modes at angles of incidence of 0°, 30°, 50°, 70°, and 90°. Get solution
18. Determine the reflectance from tin at angles of incidence of 0°, 30°, and 60°. Do this for the (a) TE and (b) TM modes of polarization. Real and imaginary parts of the complex refractive index are 1.5 and 5.3, respectively, for light of 589.3 nm. Get solution
19. a. What is the absorption coefficient for tin, with an imaginary part of the refractive index equal to 5.3 for 589.3-nm light?b. At what depth is 99% of normally incident sodium light absorbed in tin? Get solution
20. a. From the power conservation requirement, as expressed by Eq. (23-47), show that for an external reflection the transmission coefficient t must be less than 1, but for an internal reflection t′ may be greater than 1.b. Show further, using the Fresnel Eqs. (23-29) and (23-30), that as the angle of incidence approaches the critical angle, t′ must approach a value of 2 in the TE mode and 2/n in the TM mode.c. Plot the transmission coefficient t′ for an interface between glass (n = 1.5) and air. Get solution
21. A narrow beam of light (λ = 546 nm) is rotated through 90° by TIR from the hypotenuse face of a 45°–90°–45° prism made of glass with n = 1.60.a. What is the penetration depth at which the amplitude of the evanescent wave is reduced to 1/e of its value at the surface?b. What is the ratio of irradiance of the evanescent wave at 1 μm beyond the surface to that at the surface? Get solution
2. The critical angle for a certain oil is found to be 33°33′. What are its Brewster’s angles for both external and internal reflections? Get solution
3. Determine the critical angle and polarizing angles for (a) external and (b) internal reflections from dense flint glass of index n = 1.84. Get solution
4. For what refractive index are the critical angle and (external) Brewster angle equal when the first medium is air? Get solution
5. Show that the Fresnel equations, Eqs. (23-27) to (23-30), may also be expressed by ... Get solution
6. Show that Eq. (23-37) follows from Eq. (23-35). Get solution
7. Using Eqs. (23-27) through (23-30) and a computer program or a computer algebra system, reproduce Figures 23-3 and 23-5. Also, change the value of n to produce graphs for the case of external and internal reflection from diamond (n = 2.42). Get solution
8. Use a computer to calculate and plot the reflectance curves of Figure 23-4. Also plot the corresponding transmittance. Get solution
9. Use a computer to calculate and plot the phase shifts on reflection as a function of angle of incidence for θ > θc. Take n = 1/1.5 to reproduce Figure 23-6 and then make similar plots for n = 1/1.3 and n = 1/2.42. Get solution
10. A film of magnesium fluoride is deposited onto a glass substrate with optical thickness equal to one-fourth the wavelength of the light to be reflected from it. Refractive indices for the film and substrate are 1.38 and 1.52, respectively. Assume that the film is nonabsorbing. For monochromatic light incident normally on the film, determine (a) reflectance from the air–film surface; (b) reflectance from the film–glass surface; (c) reflectance from an air–glass surface without the film; (d) net reflectance from the combination. See Eq. (22-43). Get solution
11. Calculate the reflectance of water (n = 1.33) for both (a) TE and (b) TM polarizations when the angles of incidence are 0°, 10°, 45°, and 90°. Get solution
12. Light is incident upon an air–diamond interface. If the index of diamond is 2.42, calculate the Brewster and critical angles for both (a) external and (b) internal reflections. In each case distinguish between polarization modes. Get solution
13. Calculate the percent reflectance and transmittance for both (a) TE and (b) TM modes of light incident at 50° on a glass surface of index 1.60. Get solution
14. Derive Eqs. (23-29) and (23-30) for the transmission coefficients both by (a) eliminating Er from Eqs. (23-20) to (23-23) and by (b) using the corresponding equations for the reflection coefficients, together with the relationships between reflection and transmission coefficients implied by Eqs. (23-20) and (23-22). Get solution
15. Unpolarized light is reflected from a plane surface of fused silica glass of index 1.458.a. Determine the critical and polarizing angles.b. Determine the reflectance and transmittance for the TE mode at normal incidence and at 45°.c. Repeat (b) for the TM mode.d. Calculate the phase difference between TM and TE modes for internally reflected rays at angles of incidence of 0°, 20°, 40°, 50°, 70°, and 90°. Get solution
17. Determine the reflectance for metallic reflection of sodium light (589.3 nm) from steel, for which nR = 2.485 and nI = 1.381. Calculate reflectance for (a) TE and (b) TM modes at angles of incidence of 0°, 30°, 50°, 70°, and 90°. Get solution
18. Determine the reflectance from tin at angles of incidence of 0°, 30°, and 60°. Do this for the (a) TE and (b) TM modes of polarization. Real and imaginary parts of the complex refractive index are 1.5 and 5.3, respectively, for light of 589.3 nm. Get solution
19. a. What is the absorption coefficient for tin, with an imaginary part of the refractive index equal to 5.3 for 589.3-nm light?b. At what depth is 99% of normally incident sodium light absorbed in tin? Get solution
20. a. From the power conservation requirement, as expressed by Eq. (23-47), show that for an external reflection the transmission coefficient t must be less than 1, but for an internal reflection t′ may be greater than 1.b. Show further, using the Fresnel Eqs. (23-29) and (23-30), that as the angle of incidence approaches the critical angle, t′ must approach a value of 2 in the TE mode and 2/n in the TM mode.c. Plot the transmission coefficient t′ for an interface between glass (n = 1.5) and air. Get solution
21. A narrow beam of light (λ = 546 nm) is rotated through 90° by TIR from the hypotenuse face of a 45°–90°–45° prism made of glass with n = 1.60.a. What is the penetration depth at which the amplitude of the evanescent wave is reduced to 1/e of its value at the surface?b. What is the ratio of irradiance of the evanescent wave at 1 μm beyond the surface to that at the surface? Get solution
No hay comentarios:
Publicar un comentario