Question

A light ray incidents normally on one surface of an equilateral prism. The angle of deviation of the light ray is
(Refractive index of the material of the prism = $\sqrt{2}$)

• A. $60^{\circ}$
• B. $30^{\circ}$
• C. $0^{\circ}$
• D. $120^{\circ}$

Answer 1

Answer: (A)

Given, $i=0^{\circ}$
So, $\frac{\sin i}{\sin r_{1}}=\sqrt{2}$
$\frac{\sin 0^{\circ}}{\sin r_{1}} =\sqrt{2}$
$\sin r_{1}=0 \text { or } r_{1}=0$
Now, $\frac{\sin r_{2}}{\sin e}=\frac{1}{\mu}$
$\Rightarrow \sin e=\sqrt{2} \sin r_{2}$
But, $r_{1}+r_{2}=60^{\circ}$
So, $\sin e =\sqrt{2} \sin 60^{\circ}$
$=\sqrt{2} \times \sqrt{3} / 2>1$
So, light is incidenting at more than critical angle and totally internally reflected.
$\therefore $ Deviation angle $=(i+ e)-\left(r_{1}+r_{2}\right)$
$=0-60^{\circ}=60^{\circ}$ (in magnitude)