Question

The refractive index of the material of a prism is $\sqrt{2}$ and its refracting angle is ${30}^o$. One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface, if its angle of incidence on the prism is

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

Answer 1

Answer: (A)

${45}^o$

$\begin{array}{c}{\mu }_2=\sqrt{2}\\ {\gamma }_2={30}^{\circ }\\ {\mu }_1\sin i={\mu }_2\sin {\gamma }_2\end{array}$

(1) $\sin i=\sqrt{2}\sin {30}^o$

$\begin{array}{cc}\text{Sin}\theta & =\frac{1}{\sqrt{2}}\\ \theta & ={45}^{\circ }\end{array}$

So, option $A$ is correct