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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

sin1(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=sin1(18)


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