Q.
A transparent solid cylindrical rod has a refractive index of$\frac{2}{\sqrt{3}}$. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure.
The incident angle $\theta$ for which the light ray grazes along the wall of the rod is
A) $\sin^{- 1}\left( \frac{1}{2} \right)$
B) $\sin^{- 1}\left( \frac{\sqrt{3}}{2} \right)$
C) $\sin^{- 1}\left( \frac{2}{\sqrt{3}} \right)$
D) $\sin^{- 1}\left( \frac{1}{\sqrt{3}} \right)$
Explanation
(d) $\sin{C = \frac{\sqrt{3}}{2}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
[image:9_image104.emf]
$\sin{r = \sin{(90{^\circ} - C) = \cos{C = \frac{1}{2}}}}$
$\frac{\sin\theta}{\sin r} = \frac{\mu_{2}}{\mu_{1}}$
$\sin{\theta = \frac{2}{\sqrt{3}} \times \frac{1}{2}}$
$\theta = \sin^{- 1}\left( \frac{1}{\sqrt{3}} \right)\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.