Chapter #25 Solutions - Optics - Ajoy Ghatak - 1st Edition
1. (a) Calculate the number of photons emitted per second by a 5 mW
laser assuming that it emits light of wavelength 6328 Å.[Ans: 1.6 ×
1016](b) The beam is allowed to fall normally on a plane mirror.
Calculate the force acting on the mirror.[Ans: 3.3 × 10 – 11 N] Get solution
2. Assume a 40 W sodium lamp (λ ≈ 5893Å) emitting light in all directions. Calculate the rate at which the photons cross an unit area placed normally to the beam at a distance at a distance of 10 m from the source.[Ans: ≈ 1017 photons/m2-sec] Get solution
3. In the photoelectric effect, a photon is completely absorbed by the electron. Show that the laws of conservation of energy and momentum cannot be satisfied simultaneously if a free electron is assumed to absorb the photon. (Thus the electron has to be bound to an atom and the atom undergoes a recoil when the electron is ejected. However, since the mass of the atom is much larger than that of the electron, the atom picks up only a small fraction of the energy, this is somewhat similar to the case of a tennis ball hitting a heavy object, the momentum of the ball is reversed with its energy remaining almost the same.) Get solution
4. If photoelectrons are emitted from a metal surface by using blue light, can you say for sure that photoelectric emission will take place with yellow light and with violet light? Get solution
2. Assume a 40 W sodium lamp (λ ≈ 5893Å) emitting light in all directions. Calculate the rate at which the photons cross an unit area placed normally to the beam at a distance at a distance of 10 m from the source.[Ans: ≈ 1017 photons/m2-sec] Get solution
3. In the photoelectric effect, a photon is completely absorbed by the electron. Show that the laws of conservation of energy and momentum cannot be satisfied simultaneously if a free electron is assumed to absorb the photon. (Thus the electron has to be bound to an atom and the atom undergoes a recoil when the electron is ejected. However, since the mass of the atom is much larger than that of the electron, the atom picks up only a small fraction of the energy, this is somewhat similar to the case of a tennis ball hitting a heavy object, the momentum of the ball is reversed with its energy remaining almost the same.) Get solution
4. If photoelectrons are emitted from a metal surface by using blue light, can you say for sure that photoelectric emission will take place with yellow light and with violet light? Get solution
Chapter #24 Solutions - Optics - Ajoy Ghatak - 1st Edition
1. Show that in the limit of ...(i.e. at normal incidence) the
reflection coefficient is the same for parallel and perpendicular
polarizations. Get solution
2. Consider a magnetic dielectric with a permeability such that ... Show that for such a material the reflection coefficient for normal incidence is identically equal to zero. This realization is equivalent to the situation where the impedance is matched at the junction of two transmission lines. (The quantity ...can be considered as the intrinsic impedance of the medium.) Get solution
3. A right –circularly polarized beam is incident on a perfect conductor at 45°. Show that the reflected beam is left –circularly polarized. Get solution
4. Assume n1 = 1.5 and n2 = 1.0 (see Example 24.6)(a) for θ1 = 45° show that ...Similarly calculate r⊥ and t⊥.(b) On the other hand, for θ1 = 33.69° show that ... Get solution
5. Consider a right – circularly polarized beam incident on a medium of refractive index 1.6 at an angle of 60°. Calculate ... and ... and show that the reflected beam is right elliptically polarized with its major axis much longer than its minor axis. What will happen at 58°? [ Ans. ... = -0.0249, ...= -0.4581] Get solution
6. Consider a y-polarized wave incident on a glass –air interface ...at ...and at .... Write the complete expressions for the transmitted field and show that in the latter case it is an evanescent wave with depth of penetration ...equal to about 8.8 ×10 –8 m; assume λ = 6000Å. Get solution
7. For gold, at ... the complex refractive index is given by n2 = 0.166 + 3.15i. Calculate ... and show that the reflectivity at normal incidence is approximately 94%. [ Hint : Use Eq. (75) directly]. On the other hand at ... show that the reflectivity is only 39%. Get solution
8. Show that for ..., Eq. (97) takes the form ... (98)as it indeed should be. Get solution
9. Using the various equations in Sec. 24.4 calculate the transmittivity and show that... Get solution
10. Assume the third medium in Fig. 24.14 to be identical to the first medium, i.e., ...Thus...Using Eq. (97), show that... (99)where... (100)is called the coefficient of finese. Equation (99) is identical to the result derived in Sec. 16.2 while discussing the theory of the Fabry – Perot interferometer. Get solution
11. When the angle of incidence is equal to the Brewster’s angle, show that ... [as given by Eq. (21)] is equal to unity. Get solution
2. Consider a magnetic dielectric with a permeability such that ... Show that for such a material the reflection coefficient for normal incidence is identically equal to zero. This realization is equivalent to the situation where the impedance is matched at the junction of two transmission lines. (The quantity ...can be considered as the intrinsic impedance of the medium.) Get solution
3. A right –circularly polarized beam is incident on a perfect conductor at 45°. Show that the reflected beam is left –circularly polarized. Get solution
4. Assume n1 = 1.5 and n2 = 1.0 (see Example 24.6)(a) for θ1 = 45° show that ...Similarly calculate r⊥ and t⊥.(b) On the other hand, for θ1 = 33.69° show that ... Get solution
5. Consider a right – circularly polarized beam incident on a medium of refractive index 1.6 at an angle of 60°. Calculate ... and ... and show that the reflected beam is right elliptically polarized with its major axis much longer than its minor axis. What will happen at 58°? [ Ans. ... = -0.0249, ...= -0.4581] Get solution
6. Consider a y-polarized wave incident on a glass –air interface ...at ...and at .... Write the complete expressions for the transmitted field and show that in the latter case it is an evanescent wave with depth of penetration ...equal to about 8.8 ×10 –8 m; assume λ = 6000Å. Get solution
7. For gold, at ... the complex refractive index is given by n2 = 0.166 + 3.15i. Calculate ... and show that the reflectivity at normal incidence is approximately 94%. [ Hint : Use Eq. (75) directly]. On the other hand at ... show that the reflectivity is only 39%. Get solution
8. Show that for ..., Eq. (97) takes the form ... (98)as it indeed should be. Get solution
9. Using the various equations in Sec. 24.4 calculate the transmittivity and show that... Get solution
10. Assume the third medium in Fig. 24.14 to be identical to the first medium, i.e., ...Thus...Using Eq. (97), show that... (99)where... (100)is called the coefficient of finese. Equation (99) is identical to the result derived in Sec. 16.2 while discussing the theory of the Fabry – Perot interferometer. Get solution
11. When the angle of incidence is equal to the Brewster’s angle, show that ... [as given by Eq. (21)] is equal to unity. Get solution
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