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 refractive index $\frac{3}{2}$. 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 $60°$
For TIR to take place
$I>{\theta }_c$
or $\sin 60°>\frac{2mu}{3}$
or $\mu >\frac{3\sqrt{3}}{4}$