question_answer

The refractive index of the material of the prism and liquid are 1.56 and 1.32 respectively.  What will be the value of q for the following refraction                                          [BHU 2003; CPMT 2004]

A)            \[\sin \theta \ge \frac{13}{11}\]

B)            \[\sin \theta \ge \frac{11}{13}\]

C)            \[\sin \theta \ge \frac{\sqrt{3}}{2}\]

D)            \[\sin \theta \ge \frac{1}{\sqrt{2}}\]

Correct Answer: B

Solution :

                   For total internal reflection from surface \[BC\] \[\theta \ge C\Rightarrow \sin \theta \ge \sin C\]                    \[\Rightarrow \sin \theta \ge \left( \frac{1}{_{l}{{\mu }_{g}}} \right)\]                    \[\Rightarrow \] \[\sin \theta \ge \left( \frac{{{\mu }_{\text{Liquid}}}}{{{\mu }_{\text{Prism}}}} \right)\]                       \[\sin \theta \ge \left( \frac{1.32}{1.56} \right)\Rightarrow \sin \theta \ge \frac{11}{13}\]