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  4. In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index ' n '. For incident angle 60° at the side AC, the refracted light beam just grazes along face AC. The refractive index of the liquid n=(√x/4). The value of x is (Given refractive index of glass =1.5 )

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Q. 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 $=1.5$ )Physics Question Image

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Solution:

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