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. The incident angle $\theta$ for which the light ray grazes along the wall of the rod is:

1. A
   ${\sin }^{-1}\left(\frac{1}{2}\right)$
2. B
   ${\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)$
3. C
   ${\sin }^{-1}\left(\frac{2}{3}\right)$
4. D
   ${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$