Question

A ray of light incident on a transparent sphere at an angle $\pi / 4$ and refracted at an angle $r$, emerges from the sphere after suffering one internal reflection. The total angle of deviation of the ray is

• A. $\frac{3 \pi}{2}-4 r$
• B. $\frac{\pi}{2}-4 r$
• C. $\frac{\pi}{4}-r$
• D. $\frac{5 \pi}{2}-4 r$

Answer 1

Answer: (A)

According to condition given in question, ray diagram of sphere is

So, deviations are
$\delta_{1}=\frac{\pi}{4}-r$
$\delta_{2}=\pi-2 r $
$\delta_{3}=\frac{\pi}{4}-r$
Total deviation of light ray is
$\delta=\delta_{1}+\delta_{2}+\delta_{3}=\frac{3 \pi}{2}-4 r$