Question

A prism of angle $\angle BAC={45}^0$ and refractive index $\sqrt{6}$ is surrounded by medium of refractive index n. A ray of light PQ is incident on side AB of prism. The refracted ray QR is incident on side AC. The angle of incidence of ray PQ is i such that $0\le i\le {90}^0.$ Then the possible value of n such that the ray suffers no deviation by face AC of prism is :

• A. $\sqrt{2}$
• B. $1.5$
• C. $\frac{\sqrt{3}}{2}$
• D. $2.5$

Answer 1

The correct option is D $2.5$

For no deviation on face AC, ray should incident it normally.

So angle AQR is 45${}^{\circ }$ . Therefore $r_1={45}^{\circ }$ too.

Now $\eta sini=\sqrt{6}Sin45$

=> $\eta sini=\sqrt{3}$

So $\eta \ge \sqrt{3}$

only possible choice is$D.2.5$

Answer. $D)2.5$