Question

A ray of light passes through four transparent media (with refractive indices μ₁ , μ₂ , μ₃ and μ₄ ) as shown in the Fig. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB; we must have

(1) μ₁ = μ₂ 

(2) μ₂ = μ₃

(3) μ₃ = μ₄

(4) μ₁ = μ₄

Answer 1

(4) μ₁ = μ₄

Let i1 be angle of incidence of ray AB in medium of refractive index μ₁ . Let, r₁ be angle of refraction in medium 2. From Snell’s law

μ₁ sin i_I = μ₂ sin r₁ .....(1)

The angle of incidence, in medium μ₂ is r₁ . Let angle of refraction, in medium 3 be r₂ . Then

μ₂ sin i_I = μ₃ sin r₂ .....(2)

The angle of incidence in μ₃ is r₂ and angle of emergence of ray CD in medium μ₄ is i₁ (because CD is parallel to AB). Therefore