question_answer

Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index 3/2 is placed on face AC of the prism. The prism is made of glass of refractive index 3/2. The limits of \[\mu \]for which total internal reflection cannot take place on face AC is

A)  \[\frac{3\sqrt{3}}{4}>\mu >\frac{\sqrt{3}}{2}\]

B) \[\mu <\frac{3\sqrt{3}}{4}\]

C) \[\mu >\sqrt{3}\]

D) \[\mu <\frac{\sqrt{3}}{2}\]

Correct Answer: B

Solution :

[b] For total internal reflection to take place

\[\sin 60{}^\circ \ge \sin C\]

\[\sin 60{}^\circ \ge \frac{2\mu }{3}\Rightarrow \mu \le \frac{3\sqrt{3}}{4}\]

\[\Rightarrow \]            \[\mu <\frac{3\sqrt{3}}{4},\mu =\frac{3\sqrt{3}}{4}\]