In the given figure, the face A C of the equilateral prism is immersed in a liquid of refractive index ' n '. For incident angle 60^° at the side A…

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