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:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 45°
Now,
$r_1=A=30°$
and,
According to Snell's law,
$\sin i=μ\sin r$
$\sin i=\sqrt{2}\sin 30°$
$\sin i=\frac{1}{\sqrt{2}}$
$⇒i=45°$