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

• Correct answer
  A

  $\frac{3 \pi}{2}-4 r$
• B

  $\frac{\pi}{2}-4 \mathrm{r}$
• C

  $\frac{\pi}{4}-r$
• D

  $\frac{5 \pi}{2}-4 r$

Solution

$\mathrm{S}_{1}=\frac{\pi}{4}-\mathrm{r}$ $\mathrm{S}_{2}=\pi-2 \mathrm{r}$ $\mathrm{S}_{3}=\frac{\pi}{4}-\mathrm{r}$ $\mathrm{S}=\mathrm{S}_{1}+\mathrm{S}_{2}+\mathrm{S}_{3}=\frac{3 \pi}{2}-4 \mathrm{r}$

Hence, the correct answer is option: 'A'.