Question

Light is incident normally on the face $AB$ of a prism as shown in the figure. A layer of liquid of refractive index $\mu$ is applied on the face $AC$ of the prism. If the prism is made of glass of refractive index $\frac{3}{2}$ , then the limit of $\mu$ for which total internal reflection takes place on face $AC$ is

• A. $\mu <\frac{3\sqrt{3}}{4}$
• B. $\mu >\sqrt{\frac{5}{2}}$
• C. $\mu >\sqrt{2}$
• D. $\mu <\sqrt{3}$

Answer 1

Answer: (A)

For critical angle at the glass-liquid interface we have
${\mu }_{1}sinC={\mu }_{2}sin90^{\circ }$
$\Rightarrow \frac{3}{2}sinC=\mu$
$\Rightarrow sinC=\frac{2\mu }{3}$
For total internal reflection
$60^{\circ }>C$
$\Rightarrow sin60^{\circ }>sinC$
$\Rightarrow \frac{\sqrt{3}}{2}>\frac{2\mu }{3}$
$\mu <\frac{3\sqrt{3}}{4}$