Question

A ray of light is incident to 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. $\cos ^ { - 1 } \left( \frac { 1 } { \mu } \right)$

Answer 1

Answer: (D)

$\cos ^ { - 1 } \left( \frac { 1 } { \mu } \right)$

Answer 2

If $\alpha =$ maximum value of vase angle for which light is totally reflected from hypotenuse.

$( 90 - \alpha ) = C =$minimum value of angle of incidence an hypotenuse for TIR

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