A parallel beam of light is incident from air at an angle $\alpha$ on the side PQ of a right angled triangular prism of refractive index $n=\sqrt{2}$. Light undergoes total internal reflection in the prism at the face PR when $\alpha$ has a minimum value of 45°. The angle $\theta$ of the prism is

JEE Advanced · 2016 · 22 May 2016 · Paper 1 · Geometrical Optics

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 a minimum value of 45°. The angle

θ

of the prism is

(A)15°✓ Correct
(B)22.5°
(C)30°
(D)45°

Answer: (A)

Solution

At the PQ face, applying Snell's law with

α = 45°

1 \times sin 45° = 2 sin β

sin β = \frac{1}{2}

, so

β = 30°

For total internal reflection at face PR, the angle of incidence must equal the critical angle:

sin θ_{c} = \frac{1}{n} = \frac{1}{2}

, so

θ_{c} = 45°

From geometry, the angle of incidence at PR is

β + θ

. For TIR at minimum

α

β + θ = 45°

30° + θ = 45°

θ = 15°

JEE Advanced · 2016 · 22 May 2016 · Paper 1 · Single correct option

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