question_answer

The refractive indices of the material of the prism and liquid are 1.56 and 1.32 respectively. What will be the value of \[\theta \] for the following refraction?

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 \[\theta \ge C\Rightarrow \sin \theta \ge \sin C\] \[\Rightarrow \] \[\sin \theta \ge \left( \frac{1}{{{\,}_{l}}{{\mu }_{g}}} \right)\] \[\Rightarrow \] \[\sin \theta \ge \left( \frac{{{\mu }_{Liquid}}}{{{\mu }_{\Pr ism}}} \right)\] \[\sin \theta \ge \left( \frac{1.32}{1.56} \right)\Rightarrow \sin \theta \ge \frac{11}{13}\]