A transparent solid cylindrical rod has a refractive index of $\frac{4}{\sqrt{3}}$ . It is surrounded by a medium of refractive index 2. A light ray is incident at the mid point of one end of the rod as shown in the figure.

The incident angle for which the light ray grazes along the wall of the rod is:

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

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

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

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

answer is C.

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Detailed Solution

$\begin{array}{l} θ = \sin^{- 1} \sqrt{μ_{1}^{2} - μ_{2}^{2}} = \sin^{- 1} \sqrt{{(\frac{4}{\sqrt{3}})}^{2} - 2^{2}} \\ = \sin^{- 1} \sqrt{\frac{16}{3} - 4} = \sin^{- 1} \frac{2}{\sqrt{3}} \end{array}$

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