question_answer

A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism.  If m 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                      [EAMCET 2003]

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

Correct Answer: D

Solution :

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