Question

A prism having refractive index 1.414 and refracting angle ${30}^{\circ }$ has one of the refracting surfaces silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is:

• A. $0^{\circ }$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is D

$\frac{\pi }{4}$

Apply Snell’s law at AB surface

${\mu }_{1}sini={\mu }_{2}sinr$

1 sini = 1.41 sin 30

$sini=\sqrt{2}\frac{1}{2}$

$sini=\sqrt{2}\frac{1}{\sqrt{2}}$

$i={45}^{\circ }or\frac{\pi }{4}$