Question

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

• A. $\mu >\frac{\sqrt{3}}{2}$
• B. $\mu <\frac{3\sqrt{3}}{4}$
• C. $\mu >\sqrt{3}$
• D. $\mu <\frac{\sqrt{3}}{2}$

Answer 1

The correct option is B $\mu <\frac{3\sqrt{3}}{4}$

Critical angle between glass and liquid face is
$\sin {\theta }_C=\frac{\mu }{3/2}=\frac{2\mu }{3}$
Angle of incidence at face $AC$ is ${60}^{\circ }$.
For T.I.R to take place,
$i>{\theta }_C$
or $\sin {60}^{\circ }>\frac{2\mu }{3}$
or $\mu <\frac{3\sqrt{3}}{4}$