1. Tardigrade
  2. Question
  3. Physics
  4. If one face of a prism of prism angle 30° and μ=√2 is silvered, the incident ray retraces its initial path. The angle of incidence is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If one face of a prism of prism angle $30^{\circ}$ and $\mu=\sqrt{2}$ is silvered, the incident ray retraces its initial path. The angle of incidence is

Ray Optics and Optical Instruments

Solution:

It is clear from the figure that the ray will retrace the path when the refracted ray $QR$ is incident normally on the polished surface $AC$. Thus angle of refraction, $r=30^{\circ}$.
image
$\mu=\frac{\sin i}{\sin r}$
$\therefore \sin i=\mu \sin r$
$\sin i=\sqrt{2} \times \sin 30^{\circ}=\sqrt{2} \times \frac{1}{2}=\frac{1}{\sqrt{2}}$
$\therefore i=45^{\circ}$