Question

In the given figure, the face $AC$ of the equilateral prism is immersed in a liquid of refractive index ' $n$ '. For incident angle $60^{\circ }$ at the side $AC$, the refracted light beam just grazes along face $AC$. The refractive index of the liquid $n=\frac{\sqrt{x}}{4}$. The value of $x$ is_____
(Given refractive index of glass $=1.5$ )

Answer 1

Answer: 27

Using snell's law at face AC
$1.5\sin 60^{\circ }=n\times \sin 90^{\circ }$
$1.5\times \frac{\sqrt{3}}{2}=n=\frac{\sqrt{x}}{4}$
$3\sqrt{3}=\sqrt{x}$
$x=27$