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 pr 9 is m. 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. $\mu <\frac{3\sqrt{3}}{2}$
• C. $\mu >\sqrt{3}$
• D. $\mu <\frac{\sqrt{3}}{2}$

Answer 1

The correct option is B $\mu <\frac{3\sqrt{3}}{2}$



Critical angle between glass and liquid face is sin ${\theta }_c=\frac{\mu }{\frac{3}{2}}=\frac{2\mu }{3}$
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 $\mu <\frac{3\sqrt{3}}{4}$