Question

A ray of light incident normally on the first face of an equilateral prism undergoes total internal reflection at the second face if refractive index $\mu$ is

• A. less than $\frac{\sqrt{3}}{2}$
• B. less than $\frac{2}{\sqrt{3}}$
• C. more than $\frac{\sqrt{3}}{2}$
• D. more than $\frac{2}{\sqrt{3}}$

Answer 1

The correct option is D more than $\frac{2}{\sqrt{3}}$

As shown in the figure, on normal incidence at first surface, the angle of incidence at second surface is 60°.

In the border case of total internal reflection just happening,

$\mu sin{60}^{\circ }=1\times sin{90}^{\circ }$

=> $\mu =2/\sqrt{3}$

Also note that if $\mu$ is greater than this value then internal reflection always takes place.