Question

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 just grazes along face AC. The refractive index of the liquid n = `sqrtx/4`. The value of x is ______.

(Given refractive index of glass = 1.5)

Options

• 25

• 27

• 22

• 24

Answer 1

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 just grazes along face AC. The refractive index of the liquid n = `sqrtx/4`. The value of x is 27.

Explanation:

Using Snell's law at face AC

μ sin 60° = n × sin 90°

1.5 sin 60° = n × sin 90° 

1.5 × `sqrt3/2` = n = `sqrt"x"/4`

= 3`sqrt3` = x

x = 27