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°
A ray retraces its path after reflection only if it strikes the mirror normally, because then it is reflected straight back along itself. So the angle of refraction at the silvered face is zero, \( r_2 = 0 \).
For a prism the two angles of refraction add up to the angle of the prism, \( r_1 + r_2 = A \):
\( r_1 = A - r_2 = 30^\circ - 0 = 30^\circ \)
Now apply Snell’s law at the first face:
\( \sin i = \mu\sin r_1 = \sqrt{2}\times\sin30^\circ = \sqrt{2}\times\frac{1}{2} = \frac{1}{\sqrt{2}} \)
\( i = 45^\circ \)