Which colour has the maximum deviation in the dispersion of white light…

Concept — Dispersion happens because the refractive index of a transparent medium is not a single fixed number: it depends on the wavelength of the light passing through it. Cauchy's relation n = a + b/λ2 shows that n grows larger as the wavelength λ grows shorter. In a prism of refracting angle A the deviation of a ray rises steadily with the refractive index the glass presents to it — exactly, at minimum deviation, through n = sin((A + δm)/2) ÷ sin(A/2), and for a thin prism through the approximation δ ≈ (n − 1)A. On either relation, within one prism the colour that meets the largest refractive index is the colour turned through the largest angle.

Application — White light is a mixture of all visible wavelengths, so every colour in it meets a different refractive index inside the same prism:

1. The visible band runs from about 700 nm at its long-wavelength end (red) down to about 400 nm at its short-wavelength end (violet).

2. Because n = a + b/λ2, the smallest refractive index goes with the longest wavelength and the largest refractive index with the shortest wavelength. For a typical crown glass, n ≈ 1.514 at 700 nm, n ≈ 1.519 at 550 nm and n ≈ 1.532 at 400 nm.

3. Every colour crosses the same prism, so the refracting angle A is common to all of them. Both the exact minimum-deviation relation and the thin-prism approximation δ ≈ (n − 1)A increase with n, so the deviations fall in exactly the same order as the refractive indices.

4. Take a prism of refracting angle A = 10° and evaluate each ray at minimum deviation, where δm = 2 sin−1(n sin(A/2)) − A. This gives δm ≈ 5.17° for n = 1.514, δm ≈ 5.22° for n = 1.519 and δm ≈ 5.35° for n = 1.532, so the largest deviation belongs to violet, the shortest visible wavelength. The thin-prism approximation δ ≈ (n − 1)A gives 5.14°, 5.19° and 5.32° for the same three indices — different numbers, but the same ordering.

Cross-check — The band thrown on a screen in Newton's prism experiment shows the same ordering. Counting away from the direction of the incoming beam the colours appear as red, orange, yellow, green, blue, indigo, violet: red lies closest to the undeviated direction and violet lies farthest from it. The angle between those two ends, δviolet − δred, is what is called the angular dispersion of the prism.

• "More than one of the above" would need two of the named colours to share one single largest deviation, but n takes a different value at each of the three wavelengths, so their deviations are all distinct.

• "None of the above" would put the most deviated colour outside the named list, but the short-wavelength end of the visible spectrum — the end where n is greatest — is itself one of the named colours.

Hence the colour that undergoes the maximum deviation when white light is dispersed by a prism is violet.