A ray of light experiences a minimum deviation when passing through an equilateral triangular glass prism…

Analyze the question: A ray passes through an equilateral prism (A = 60°) at minimum deviation. We need the angle of incidence, given n = 1.5.

Concept: At minimum deviation, the ray passes symmetrically through the prism, so the angle of incidence equals the angle of emergence (i = e), and the refraction angle inside is r = A/2.

The prism formula is:

n = sin i / sin r, where r = A/2

Solution:

1. A = 60°, so r = A/2 = 30°
2. sin i = n × sin r = 1.5 × sin 30° = 1.5 × 0.5 = 0.75
3. i = sin⁻¹(0.75) ≈ 48.6°

Check with the other formula: n = sin[(A + D)/2] / sin(A/2), so (A + D)/2 = i = 48.6°. This gives D = 2(48.6°) − 60° = 37.2°, which is a sensible deviation.

Eliminating the other options:

• 300° and 105° are impossible for an angle of incidence (it must be less than 90°).
• 60° would give n = sin 60°/sin 30° = 1.73, not 1.5.
• 75.5° would give sin 75.5° = 0.968, so n = 1.94, which is also wrong.

Tip: At minimum deviation, always remember r = A/2 and i = e. For an equilateral prism, r = 30° and sin 30° = 0.5, so sin i = n/2. Here that is 1.5/2 = 0.75. Memorize that sin⁻¹(0.75) ≈ 48.6°.