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:
15∘
45∘
30∘
22.5∘
A
30∘
B
45∘
C
22.5∘
D
15∘
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Solution
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Applying Snell's law at surface PQ, ∴1×sinα=n×sinβ at α=45°,n=√2 sinβ=12∴β=30° γ=90−(180−(90+θ+β)) ∴ Applying Snell's law at surface PR ∴√2sinγ=1 ∴sin(θ+β)=1√2 ∴θ+β=45° ∴θ+30°=45° ∴θ=15° Thus option A
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