The exit surface of a prism with refractive index n is coated with a material having refractive index n/2. When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle i $s____$
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Question

The exit surface of a prism with refractive index n is coated with a material having refractive index n/2. When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle i $s____$

Options

G1 Physics · Accepted Answer

At minimum deviation, i = e and the refraction angles inside the prism are equal: r₁ = r₂ = A/2. At the coated exit surface, the ray is exactly at the critical condition. Therefore, r₂ = c. For light travelling from refractive index n to n/2, sin c = (n/2)/n = 1/2. Hence, c = 30°. Therefore, A/2 = 30°, so A = 60°. Correct option: A.

The exit surface of a prism with refractive index n is coated with a material having refractive index n/2. When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle i s____