Q. 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
A) $\sin^{- 1}\left( \frac{1}{\mu} \right)$
B) $\tan^{- 1}\left( \frac{1}{\mu} \right)$
C) $\sin^{- 1}\left( \frac{\mu - 1}{\mu} \right)$
D) $\cos^{- 1}\left( \frac{1}{\mu} \right)$
Explanation
(d) For total internal reflection
$\mu = \frac{1}{\sin C}$
$\mu = \frac{1}{\sin{(90{^\circ} - \theta)}}$
$\mu = \frac{1}{\cos\theta} \Rightarrow \cos\theta = \frac{1}{\mu}$
$\theta = \ \cos^{- 1}\left( \frac{1}{\mu} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.