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 $=\frac{3}{2}$
$\Rightarrow \mu_{L}=\frac{3}{2} \sin 60^{\circ}=\left(\frac{3}{2}\right)\left(\frac{\sqrt{3}}{2}\right)$
$=\frac{3 \sqrt{3}}{4}$