A ray undergoes a minimum deviation at 40o when it is incident on equilateral triangular glass prism. Calculate the refractive index of the prism

Analyze the question

A ray passes through an equilateral prism, so the prism angle is A = 60°. The minimum deviation is D = 40°. We need the refractive index n.

Concept

At minimum deviation, the prism formula is:

n = sin[(A + D)/2] / sin(A/2)

Solution

1. (A + D)/2 = (60° + 40°)/2 = 50°
2. A/2 = 30°
3. n = sin 50° / sin 30°
4. sin 50° = 0.7660 and sin 30° = 0.5
5. n = 0.7660 / 0.5 = 1.532

So n ≈ 1.53.

Answer

Tip

For minimum deviation questions, remember that sin 30° = 0.5, so the answer is simply 2 × sin[(A + D)/2]. Learn sin 50° ≈ 0.766, sin 45° ≈ 0.707 and sin 60° ≈ 0.866 so you can work quickly without tables. Also, "equilateral prism" always means A = 60°.