Question

The face $PR$ of a prism $QPR$ of angle ${30}^o$ is silvered. A ray incident on face $PQ$ at an angle of ${45}^o$ as shown in the figure. The refracted ray undergoes reflected on face $PR$ and retraces its path. The refractive index of the prism is

• A. $\surd 2$
• B. $3/\surd 2$
• C. $1.5$
• D. $1.33$

Answer 1

The correct option is A $\surd 2$

From the image it is clear that,

for the light to retrace its path,

it should fall normally on the mirror.

and for a normal fall on the mirror,

${90}^0-r+{90}^0+{30}^0={180}^0$

$r={30}^0$

By snellls law,

${\mu }_{air}\sin {45}^0=\mu \sin {30}^0$ ${\mu }_{air}=1$

$\mu =\frac{\sin {45}^0}{\sin {30}^0}=\frac{2}{\sqrt{2}}=\sqrt{2}$

Hence option $\text{A}$ is the correct answer.