question_answer

A ray of light while travelling from a denser to a rarer medium undergoes total reflection. Derive the expression for the critical angle in terms of the speed of light in the respective media.                                          

Answer:

                Using Smell?s law for refraction from glass to air, \[\frac{\sin i}{\sin r}{{=}^{g}}{{\mu }_{a}}=\frac{\upsilon }{c}\] where c is the speed of light in air and v is the speed of light in glass. In the condition of critical incidence, we have \[i={{i}_{c}}\]     and \[r={{90}^{\circ }}\] \[\therefore \]  \[\frac{\sin {{i}_{c}}}{\sin {{90}^{\circ }}}=\frac{\upsilon }{c}\] or \[\sin {{i}_{c}}=\frac{\upsilon }{c}\] or            \[{{i}_{c}}={{\sin }^{-1}}\left( \frac{\upsilon }{c} \right).\]