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
B
22.5
C
30
D
45

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=12∴β=30° for total internal reflection (TIR), 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 matches correctly.   Co-Curriculars

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