Question

A ray of light is incident at an angle of 60º on one face of a prism which has an angle of 30º. The ray emerging out of the prism makes an angle of 30º with the incident ray. Show that the emergent ray is perpendicular to the face through which it emerges and calculate the refractive index of material of the prism.

(a) μ = √2

(b) μ = √3

(c) μ = √4/3

(d) none

Answer 1

Correct Option :- (b) μ = √3 

Explanation :-

According to given problem A = 30º, i₁ = 60º, δ = 30º 

In a prism δ = (i₁ + i₂) – (r₁ + r₂) 

δ = (i₁ + i₂) – A 

30 = 60 + i₂ -30 

i₂ =0 

So the emergent ray is ⏊ to the face from which it emerges 

Now as i₂ =0, r₂ =0 but r₁ + r₂ = A 

r₁ +0 = 30 

r₁ = 30 

So at first face 1 sin 60 = μ sin 30 

√3/2 = μ(1/2) 

μ = √3 Answer