Refraction through a prism
A prism has two refracting faces meeting at the angle of the prism, A. A ray entering one face at angle i refracts (angle r₁), meets the second face at r₂ and leaves at angle e. The geometry gives: r₁ + r₂ = A The total angle of deviation is: δ = i + e – A
Minimum deviation
As i increases, δ first decreases, reaches a minimum value D_m, then increases. At minimum deviation the ray passes symmetrically: i = e and r₁ = r₂ = A/2, and the ray inside is parallel to the base (for an isosceles prism). Then: n = sin[(A + D_m)/2] / sin(A/2) For an equilateral prism (A = 60°) with D_m = 30°: n = sin 45° / sin 30° = √2 ≈ 1.41.
Thin prism
For a small prism angle, the deviation is approximately: δ = (n – 1)A A thin prism of A = 5° and n = 1.5 deviates light by 2.5°.
Dispersion
White light passing through a prism splits into its colours: violet, indigo, blue, green, yellow, orange, red (VIBGYOR from the base side up to the apex side). This is dispersion. It happens because the refractive index of glass depends on wavelength: it is larger for shorter wavelengths, so violet is deviated most and red least. In vacuum all colours travel at the same speed; in glass violet travels slowest.
The angle between the emerging violet and red rays from a thin prism is the angular dispersion: δ_v – δ_r = (n_v – n_r)A. For A = 6°, n_v = 1.66 and n_r = 1.64, it is 0.02 × 6 = 0.12°.
The rainbow is a natural example: dispersion, refraction and internal reflection in raindrops.
Key points
- r₁ + r₂ = A; δ = i + e – A.
- At minimum deviation, i = e and r₁ = r₂ = A/2.
- n = sin[(A + D_m)/2] / sin(A/2).
- Thin prism: δ = (n – 1)A.
- Violet deviates most, red least.
Exam tips
- When asked for r inside an equilateral prism at minimum deviation, answer 30° immediately.