question_answer

A light wave travels from glass to water. The refractive indices for glass and water are\[\frac{3}{2}\]and\[\frac{4}{3}\] respectively. The value of the critical angle will be:

A) \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]                

B) \[{{\sin }^{-1}}\left( \frac{9}{8} \right)\]

C) \[{{\sin }^{-1}}\left( \frac{9}{8} \right)\]                

D) \[{{\sin }^{-1}}\left( \frac{5}{7} \right)\]

Correct Answer: C

Solution :

From the relation, \[\frac{1}{\sin C}{{=}_{\omega }}{{\mu }_{g}}\] Or           \[\frac{1}{\sin C}=\frac{{{\mu }_{g}}}{{{\mu }_{\omega }}}\]        where\[C=\]critical angle \[{{\mu }_{g}}=\]refractive index of glass\[=\frac{3}{2}\] \[{{\mu }_{\omega }}=\]refractive index of water\[=\frac{4}{3}\] \[\therefore \]  \[\sin C=\frac{{{\mu }_{\omega }}}{{{\mu }_{g}}}\]                 \[\sin C=\frac{4/3}{3/2}\]                 \[\sin C=\frac{8}{9}\] Hence,    \[C={{\sin }^{-1}}\left( \frac{8}{9} \right)\]