A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base…
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
$\sin ^{-1}\left(\frac{1}{\mu}\right)$
$\tan ^{-1}\left(\frac{1}{\mu}\right)$
$\sin ^{-1}\left(\frac{\mu-1}{\mu}\right)$
$\cos ^{-1}\left(\frac{1}{\mu}\right)$
Solution
For total internal reflection,
$\mu=\frac{1}{\sin C}$
$\mu=\frac{1}{\sin \left(90^{\circ}-\theta\right)}$
$\mu=\frac{1}{\cos \theta} \Rightarrow \cos \theta=\frac{1}{\mu}$
$\theta=\cos ^{-1}\left(\frac{1}{\mu}\right)$
