Question

A light ray is incident normally on the surface ab of a prism of refracting angle 60.If the light ray does not emerge from ac, then the refractive index of the prism

Answer 1

The refractive index of the prism is μ > 2 / √3

Explanation:

Here for no emergence through Ac, TIR Happens at AC.

μsin ( i) > 1 x sin 90°

or μ > 1 / sin (i)

or μ > 1/ sin (60°)

or  μ > 2 / √3

Thus the refractive index of the prism is μ > 2 / √3.

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Answer 2

Since no emergence takes place, so sine of refracted angle(here as incident angle for the next surface) is greater than sine of critical angle

sinr>sinθ

sin 60°>sinθ

sin60°>1/μ

√3/2>1/μ

μ>2/√3

So, the refractive index of glass slab should be greater than 2/√3.