A monochromatic red light (λ = 600 nm) and violet light (λ = 400 nm) pass through a prism whose apex angle is 30°. The refractive index of the prism for red light is 1.50 and for violet light is 1.55. Assuming small angles, calculate the angular dispersion between the red and violet rays after emerging from the prism.

Step-by-step solution

1. For small angles, the deviation δ of a ray by a prism can be approximated by δ ≈ (n – 1)·A, where n is the refractive index and A is the apex angle.
2. Calculate deviation for red light: δ_red = (1.50 – 1) × 30° = 0.50 × 30° = 15°.
3. Calculate deviation for violet light: δ_violet = (1.55 – 1) × 30° = 0.55 × 30° = 16.5°.
4. Angular dispersion = δ_violet – δ_red = 16.5° – 15° = 1.5°.

Concept tested: Dispersion of light by a prism

Published 25 August 2026 · How this solution was prepared and checked

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