Q83 / 90 · JEE Main 2022 (26 Jul Shift 2) · Physics

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=x4. The value of x is _____ .
(Given refractive index of glass =1.5)

Figure

Correct answer: 27

Solution

Figure

When the refracted light just grazes the boundary the incident angle is called a critical angle.

Using snell's law at face AC.

1.5sin60°=n×sin90° 

⇒1.5×32=n=x4 

⇒33=x

⇒x=27

Hence, the correct answer is 27.

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