Question

# A beam of light is traveling from Region I to Region IV (refer figure). The refractive index of Region I, II, III and IV are n0,n02,n06andn08 respectively. The angle of incidence θ for which the beam just misses entering Region IV is:

A

sin1(34)

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B

sin1(18)

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C

sin1(14)

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D

sin1(13)

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Solution

## The correct option is B sin−1(18) When a light ray enters from medium 1 to medium 2, by snell's law we know that, sin θsin r=absolute refractive index medium 2absolute refractive index medium 1 For first interface, sin θsin r=n02×n0=12 (1) For second interface, sin rsin r1=n0×26×n0=13 (2) For the light to just miss entering region IV sin r1sin 90=n0×68×n0=34 (3) putting sin r1 in (2) sin r=13×34=14 putting this value in (1) sin θ=12×14=18 ∴ θ=sin−1(18)

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