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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 μ=√2. Light undergoes total internal reflection at the face PR when α has a 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∘Given: Refractive index of air, μair=1 Refractive index of prism, μprism=√2 Applying snell's law at face PQ μair sinα=μprism sinr1 Substituting the given data we get, 1×sinα=√2×sinr1 ⇒1×sin45∘=√2×sinr1 [For, α=45∘] ∴r1=30∘ Critical angle for glass-air interface, sinθc=1μ=1√2 ∴θc=45∘ From, ΔPLM: θ=180∘−(90∘+r1+90∘−θc) ⇒θ=θc−r1 ⇒θ=45∘−30∘=15∘ Hence, option (a) is the correct answer.

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