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 $n = \frac{\sqrt{x}}{4}$ . The value of x is_________ .
(Given refractive index of glass = 1.5)

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answer is 27.

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Detailed Solution

Using snell’s law at face AC

$\begin{array}{l} 1 .5 \sin 60^{\circ} = n \times \sin 90^{\circ} \\ 1 .5 \times \frac{\sqrt{3}}{2} = n = \frac{\sqrt{x}}{4} \\ 3 \sqrt{3} = \sqrt{x} \\ x = 27 \end{array}$

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