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 :

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

$\text{Step 1: }$ 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 ,

$\theta =si{n}^{-1}\left(\frac{1}{\mu }\right)$

From diagram
$\alpha +\theta =90^o$

$\Rightarrow \alpha =90^o-si{n}^{-1}\left(1/\mu \right)=co{s}^{-1}\left(1/\mu \right)$

$\text{Correct option: D}$