Q. A prism having refractive index 1.414 and refractive angle $30{^\circ}$has one of the refracting surfaces silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is
A) $45{^\circ}$
B) $60{^\circ}$
C) $30{^\circ}$
D) $0{^\circ}$
Explanation
(a) $r₂\ = \ 0$ ($\because$ No refraction is there at second surface)
$\therefore\ \ r_{1} = A = 30{^\circ}$
$n = \frac{\sin{i₁}}{\sin{r₁}} = \frac{\sin{i₁}}{\sin{30{^\circ}}} = \sqrt{2} \times \frac{1}{2} = \frac{1}{\sqrt{2}}$
$\sin{i₁\ = \frac{1}{\sqrt{2}}}$
$i₁\ = 45{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.