Question

A light ray incident normally on one face of an equilateral prism and emerges out grazingly at the other face. The refractive index of the prism is : -

• A. $\sqrt{3}$
• B. $\sqrt{2}$
• C. $\frac{2\sqrt{3}}{5}$
• D. $\frac{2}{\sqrt{3}}$

Answer 1

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

The ray incident normally on the first surface of the prism do not suffer refraction and falls on the second surface$.$

from the triangle $ABC$

$90+60+x=180$

$x=30$

Angle of incidence on the net surface is $=(90-30)={60}^0$

Applying snells law on the next surface of the prism

$\begin{array}{c}\mu \times \sin i=1\times \sin r\\ \mu \times \sin {60}^0=1\times \sin {90}^0\\ \mu \times \frac{\sqrt{3}}{2}=1\\ \mu =\frac{2}{\sqrt{3}}\end{array}$

Hence,

option $\left(D\right)$ is correct answer.