Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index $\mu$ is placed on the face AC of the prism. The prism is made of glass of refractive index 3/2. The limit of $\mu$ for which total internal reflection takes place on face AC is :

Critical angle for glass-liquid :

$_a\mu_g\, sin \, C=_a\mu _i\, sin 90^o$

$\Rightarrow \dfrac{3}{2} sin \, C=\mu \times 1$

$\Rightarrow sin \, C =\dfrac{2\mu}{3}$

For Total Internal reflection on AC,

We must have $60^o \geq C$

$\Rightarrow sin 60^o \geq sin \, C$

$\Rightarrow \dfrac{\sqrt{3}}{2}\geq \dfrac{2 \mu}{3}$

Thus, we get $\mu\leq \dfrac{3\sqrt{3}}{4}$