Question

A prism having refractive index $\sqrt{2}$ and refracting angle ${30}^{\circ }$, has one of the refracting surface polished. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is :

• A. $0^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$


For the ray to retrace its path, it should be incident normally,
Hence $r={30}^{\circ }$
By snell's law,
${\mu }_1\sin i={\mu }_2\sin r$
$1\sin i=\sqrt{2}\sin {30}^{\circ }=\sqrt{2}\times \frac{1}{2}$
$i={\sin }^{-1}\left(\frac{1}{\sqrt{2}}\right)$
$i={45}^{\circ }$