Question

Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index μ is placed on face AC of the prism. The prism is made of glass of refractive index 3/2 . The limits of 'μ'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
$\sin {\theta }_c=\frac{\mu }{\left(\frac{3}{2}\right)}$

$=\frac{2\mu }{3}$

Angle of incidence at face $AC$ is ${60}^{\circ }$


For TIR to take place.

$i>{\theta }_c$

or $\sin {60}^{\circ }>\frac{2\mu }{3}$

or $\mu <\frac{3\sqrt{3}}{4}$