A ray of light is incident normally on one of the refracting surface of a prism of refracting angle A . The emergent ray grazes the other refracting surface. Find the refractive index of the material of prism.

Q: A ray of light is incident normally on one of the refracting surface of a prism of refracting angle A . The emergent ray grazes the other refracting surface. Find the refractive index of the material of prism.

Sol: For normal incidence on one of the refracting faces of the prism, i1 = 0 and r1 = 0.

But , r1 + r2 = A when light undergoes refraction through a prism.

0 + r2 = A; r2 = A

When the emergent light grazes the second surface, r2 becomes the critical angle (C)

i.e. C = A and μ = 1/sin⁡C = 1/sin⁡A