Question

A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is \(\sqrt{3}\), then the angle of incidence is:

• A. \(60^{\circ}\)
• B. \(45^{\circ}\)
• C. \(90^{\circ}\)
• D. \(30^{\circ}\)

Hint:

At minimum deviation the ray passes symmetrically, so \(r = A/2 = 30^{\circ}\); apply Snell's law at the first face.

Answer 1

The Correct Option is A

For an equilateral prism \(A = 60^{\circ}\). At minimum deviation \(i = e\) and \(r_1 = r_2 = A/2 = 30^{\circ}\).
Snell's law at the first face: \(\sin i = \mu \sin r_1 = \sqrt{3}\sin 30^{\circ} = \sqrt{3}\times\frac{1}{2} = \frac{\sqrt{3}}{2}\).
So \(i = 60^{\circ}\).
Answer: (1) \(60^{\circ}\)