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 C , the refracted light beam just grazes along face A C

Question

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 C , the refracted light beam just grazes along face A C . The refractive index of the liquid n = x 4 . The value of x is _____ . (Given refractive index of glass = 1 . 5 )

TestHub · Accepted Answer

When the refracted light just grazes the boundary the incident angle is called a critical angle.
Using snell's law at face $A C$ .
$1.5 \sin 60 ° = n \times \sin 90 °$
$\Rightarrow 1.5 \times \frac{\sqrt{3}}{2} = n = \frac{\sqrt{x}}{4}$
$\Rightarrow 3 \sqrt{3} = \sqrt{x}$
$\Rightarrow x = 27$

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