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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=12

θc=45



From, ΔPLM:

θ=180(90+r1+90θc)

θ=θcr1

θ=4530=15

Hence, option (a) is the correct answer.

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