Question

The refractive index of the material of a prism in $\sqrt{2}$ and its refractive 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, then the angle of incidence on the prism is:

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

Answer 1

Answer: (D)

${45}^o$

The path will be retraced only if the

incident ray is normal on hitting the mirror

$x-90-60={30}^{\circ }$

${\mu }_{1}sini={\mu }_2\sin \gamma$

$1\times \sin i=\sqrt{2}\sin 30$

is $\sin i=\frac{1}{\sqrt{2}}$

$i={45}^{\circ }$

Hence option (D) is correct