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 midpoint of one end of the rod as shown in the figure.

The incident angle $\mathrm{\theta }$ for which the light ray grazes along the wall of the rod is

• A

  ${\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

• B

  ${\sin }^{-1}\left(\frac{2}{\sqrt{3}}\right)$

• C

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

• D

  ${\sin }^{-1}\left(\frac{1}{2}\right)$