Question

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. $si{n}^{-1}\left(\frac{1}{\mu }\right)$
• 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 form hypotenuse.

${90}^{\circ }-\alpha$ = C = minimum value of angle of incidence at hypotenuse for total internal reflection
$sin({90}^{\circ }-\alpha )=sinC=\frac{1}{\mu }\Rightarrow cos\alpha =\frac{1}{\mu }\Rightarrow \alpha =co{s}^{-1}\left(\frac{1}{\mu }\right)$