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Question:

A ray of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60° (see figure). If the refractive index of the material of the prism is √3, which of the following is (are) correct?

The ray comes out through face AD

The ray gets totally internally reflected at face CD

The angle between the incident ray and the emergent ray is 120°

The angle between the incident ray and the emergent ray is 90°

Solution:

Using Snell's law at surface AB:

sin i / sin r = μ

sin 60° / sin r = √3

sin r = sin 60° / √3 = (√3/2) / √3 = 1/2

r = 30°

Angle of prism A = 60°

Angle of refraction at AB = 30°

Angle of incidence at AD = 60° - 30° = 30°

Angle of refraction at AD = 60°

The ray comes out through face AD.

At surface AC:

Angle of incidence = 30°

Critical angle = sin⁻¹(1/√3) ≈ 35.26°

Since the angle of incidence (30°) is less than the critical angle, total internal reflection does not occur.

Angle between incident ray and emergent ray = 180° - 60° = 120°