The refractive index of the material of a prism is $\sqrt{2}$ and angle of prism is 30°. One of the two refracting surface of the prism is made a mirror inwards, by silver coating at outer surface. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is:

45°

The correct answer is Option (2) → 45°

Now,

$r_1=A=30°$

and,

According to Snell's law,

$\sin i=μ\sin r$

$\sin i=\sqrt{2}\sin 30°$

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

$⇒i=45°$