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Question

A parallel beam of light is incident from air at an angle α on the side PQ of a right-angled  triangular prism of refractive index n=2. Light undergoes total internal reflection in the prism at the face PR when  α has minimum value of 45. The angle θ of the prism is


A
15
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B
22.5
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C
30
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D
45
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Solution

The correct option is A 15

Applying Snell's law at surface PQ,
n1×sinα=n2×sinβ
1×sinα=n×sinβ
at α=45°,n=2
sinβ=12β=30°
for total internal reflection (TIR),
γ=90(180(90+θ+β))

Applying Snell's law at surface PR
2sinγ=1
sin(θ+β)=12
θ+β=45°
θ+30°=45°
θ=15°
Thus option A matches correctly. 

 

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