Question

A rectangular block is composed of three different glass prisms (with refractive indices µ₁, µ₂ and µ₃) as shown in the figure below. A ray of light incident normal to the left face emerges normal to the right face. Then, the refractive indices are related by

(a) µ₁² + µ₂² = 2µ₃²

(b) µ₁² + µ₂² = µ₃²

(c) µ₁² + µ₃² = 2µ₂²

(d) µ₂² + µ₃² = 2µ₁²

Answer 1

Answer is : (c) µ₁² + µ₃² = 2µ₂²

Ray diagram of ray through the composition of prisms will be

By Snell’s law on surface AB and AC, we

Squaring and adding Eqs (i) and (ii),

we get \(\frac{\mu^2_1}{2}+\frac{\mu^2_3}{2}=\mu^2_2\)