Chapter #17 Solutions - Optics - Ajoy Ghatak - 1st Edition

1. The orange Krypton like (λ = 6058 Å) has a coherence length of ~20 cm. Calculate the line width and the frequency stability.[ Ans. ~ 0.01 Å, ~ 1.5 × 10-6] Get solution

2. Laser linewidths as low as 20Hz have been obtained. Calculate the coherence length and the frequency stability. Assume λ = 6328 Å. Get solution

3. In Sec. 17.4 we had mentioned that the lateral coherence width of a circular source is 1.22λ/θ. It can be shown that for good coherence (i.e. for a visibility of 0.88 or better), the coherence width should be ƒ 0.3λ/θ. Assuming that the angular diameter of the sun is about 30′, calculate the distance between two pinholes which would produce a clear interference pattern.[ Ans. ~ 0.02 mm] Get solution

4. Calculate the distance at which a source of diameter 1 mm should be kept from a screen so that two points separated by a distance of 0.5 mm may be said to be coherent. Assume λ = 6×10-5 cm. Get solution

5. In a Michelson interferometer experiment, it is found that for a source S, as one of the mirrors is moved away from the equal path length position by a distance of about 5 cm, the fringes disappear. What is the coherence time of the radiation emerging from the source? Get solution

6. If we perform the Young’s double-hole experiment using white light, then only a few coloured fringes are visible. Assuming that the visible spectrum extends from 4000 to 7000 Å, explain this phenomenon qualitatively on the basis of coherence length. Get solution

7. Using the stellar interferometer, Michelson observed for the star Betelgeuse, that the fringes disappear when the distance between the movable mirrors is 25 inches. Assuming λ ≈6×10-5 cm, calculate the angular diameter of the star. Get solution

8. Consider Young’s double-hole experiment as shown in Fig. 17.5. The distance SS1 ≈ 1 m. Calculate the angular diameter of the hole S which will produce a good interference pattern on the screen. Assume λ = 6000 Å. Get solution

9. Assume a Gaussian pulse of form... Show that the Fourier transform is given by... You will have to use the following integral [see Appendix A]...Show that the temporal coherence is ~τ. Assume τ >> (1/ω0), plot the Fourier transform A(ω) [as a function of ω] and interpret it physically. Show that the frequency spread Δω ~1/τ. Get solution

10. In Problem 17.9, assume λ0 = 6×10-5 cm and τ ~10-9 sec. Calculate the frequency components predominantly present in the pulse and compare it with the case corresponding to τ ~10-6 sec. Get solution


Chapter #30 Solutions - Optics - Ajoy Ghatak - 1st Edition

1. Get solution 2. Get solution 3. Get solution 4. Get solution 5. Get solution