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. $si{n}^{-1}\left(\frac{1}{\mu }\right)$
• B. $ta{n}^{-1}\left(\frac{1}{\mu }\right)$
• C. $si{n}^{-1}\left(\frac{\mu -1}{\mu }\right)$
• D. $co{s}^{-1}\left(\frac{1}{\mu }\right)$

Answer 1

The correct option is D $co{s}^{-1}\left(\frac{1}{\mu }\right)$

If $\alpha$= maximum value of base angle for which light is totally reflected from hypotenuse.
$(90-\alpha )=C$=minimum value of angle of incidence an hypotenuse for TIR
$sin(90-\alpha )=sinC=\frac{1}{\mu }\Rightarrow \alpha =co{s}^{-1}\left(\frac{1}{\mu }\right)$