Question 73 of 295

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$\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)$

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Answer: (D) $\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$$\begin{aligned} & \sin c=\frac{\sqrt{3}}{2} \\ & \sin r=\sin (90-c)=\cos c=\frac{1}{2} \\ & \frac{\sin \theta}{\sin r}=\frac{\mu_2}{\mu_1} \\ & \sin \theta=\frac{2}{\sqrt{3}} \times \frac{1}{2} \\ & \theta=\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \end{aligned}$$