Question

A ray of light is incident normally on the prism $\left(\mu =\frac{3}{2}\right)$ immersed in a liquid as shown in the figure. The largest value for the angle $\alpha$ so that ray is totally reflected at the face $AC$ is $30^{\circ }$. The refractive index of the given liquid is

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

Answer 1

Answer: (D)

$\alpha +C=90^{\circ }$
$\Rightarrow C=90^{\circ }-30^{\circ }=60^{\circ }$

For total internal reflection at point $P$
${\mu }_g\sin C={\mu }_L$
Where, ${\mu }_g=$ Refractive index of the prism $=\frac{3}{2}$
$\Rightarrow {\mu }_L=\frac{3}{2}\sin 60^{\circ }=\left(\frac{3}{2}\right)\left(\frac{\sqrt{3}}{2}\right)$
$=\frac{3\sqrt{3}}{4}$