A light beam is travelling from Region I to Region IV (refer figure). The refractive index in Region 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

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TestHub · Accepted Answer

Critical angle from region III to region IV sin θ c ​ = n 0 ​ /6 n 0 ​ /8 ​ = 4 3 ​ Now applying Snell's law in region I and region III : n 0 ​ sin θ = 6 n 0 ​ ​ sin θ c ​ or sin θ θ ​ = 6 1 ​ sin θ c ​ = 6 1 ​ ( 4 3 ​ ) = 8 1 ​ = sin − 1 ( 8 1 ​ ) ​ ∴ correct option is (b).

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