SATHEE: Optics 7 Question 13

Optics 7 Question 13

13. A light beam is travelling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are $n_{0}, \frac{n_{0}}{2}, \frac{n_{0}}{6}$ and $\frac{n_{0}}{8}$ , respectively. The angle of incidence $θ$ for which the beam just misses entering Region IV is

(2008, 3M)

(a) $\sin^{- 1} \frac{3}{4}$

(b) $\sin^{- 1} \frac{1}{8}$

(d) $\sin^{- 1} \frac{1}{3}$

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Solution:

Critical angle from region III to region IV

$\sin θ_{C} = \frac{n_{0} / 8}{n_{0} / 6} = \frac{3}{4}$

Now, applying Snell’s law in region I and region III

$\begin{aligned} n_{0} \sin θ & = \frac{n_{0}}{6} \sin θ_{C} \\ or \sin θ & = \frac{1}{6} \sin θ_{C} \\ = \frac{1}{6} \frac{3}{4} = \frac{1}{8} \\ ∴ θ & = \sin^{- 1} \frac{1}{8} \end{aligned}$

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Optics 7 Question 13

13. A light beam is travelling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are n0,n02,n06 and n08, respectively. The angle of incidence θ for which the beam just misses entering Region IV is

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13. A light beam is travelling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are $n_{0}, \frac{n_{0}}{2}, \frac{n_{0}}{6}$ and $\frac{n_{0}}{8}$ , respectively. The angle of incidence $θ$ for which the beam just misses entering Region IV is