A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If $\mu$ is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is :

$\textbf {Hint :}$ Use critical angle $C=\sin^{-1}\left(\dfrac{1}{\mu}\right)$

$\textbf{Step 1: }$ Calculating the maximum value of the base angle $\alpha$

If $\alpha$ is maximum value of base angle for which light is totally reflected from the hypotenuse and $\theta$ is the minimum value of angle of incidence at hypotenuse for total internal reflection.

Then ,

$\theta =sin^{-1}\left ( \dfrac{1}{\mu}\right )$

From diagram

$\alpha +\theta =90^o$

$\Rightarrow \alpha = 90^o-sin^{-1}\left ( 1/\mu \right )=cos^{-1}\left ( 1/\mu \right )$

${\textbf{Correct option: D}}$