Question

A glass prism has refractive index $\sqrt{2}$ and refracting angle ${30}^{\circ }$. One of the refracting surface of the prism is silvered. A beam of monochromatic light will retrace it path if its angle of incidence on the unsilvered refracting surface of the prism is

• A. $0$
• B. $\pi /6$
• C. $\pi /4$
• D. $\pi /3$

Answer 1

The correct option is C $\pi /4$

For the ray to retrace back , it should incident normal to the mirror

$r^{{}^{\prime }}=0$

$r=A-r^{{}^{\prime }}=30-0={30}^0$

Applying Snell's law at first surface

${\mu }_{1}sin{\alpha }_1={\mu }_{2}sin{\alpha }_2$

$1\times sini=\sqrt{2}sin{30}^0$

$i={45}^0$

option $C$ is correct