The Violet the Eye Throws Away

Rayleigh scattering goes as the inverse fourth power of wavelength. Violet, the shortest light we see, is scattered more than blue — and about ten times more than red. So the daytime sky should be violet. It is blue. The catch is hidden in the word should: a colour is not the brightest wavelength — it is the single answer your eye folds the whole spectrum down to. Build the sky's colour from the scattered sunlight below and watch where it lands.

Here is the argument everyone half-remembers, and it is almost right:

1. Air scatters short wavelengths far more than long ones — Rayleigh's law, intensity ∝ λ⁻⁴. 2. Violet is the shortest wavelength we can see, so the scattered light coming from the empty sky is brightest in the violet. 3. Therefore the sky is violet.
Step 3 is the slip. The light really is brightest in the violet — you can read that off the curve below. But "what colour is this light?" is a different question from "which wavelength is brightest?", and the eye answers the first one.

Build the sky's colour

Scattering strength — intensity ∝ λ^−p, with p = 4.0

p = 0 is the bare Sun (no sky). p = 4 is real Rayleigh scattering — the clear daytime sky. Drag it and watch both answers move.

The naive answer

"What's the brightest wavelength?"

↳ the wrong question

What the eye does

"What colour is this whole spectrum?"

↳ the sky

Where the answers land on the map of all colours (CIE 1931):

white (equal energy)

the eye's verdict — the sky

pure violet, where the naive answer points

The sky's dot never reaches the violet corner, no matter how hard you scatter.

Crank the slider all the way to p = 6 — scatter the violet six times as ferociously as a fourth power. The "brightest wavelength" answer marches off into deep violet. The eye's answer barely stirs: it deepens from a pale to a richer blue and stops. The reason is structural. Your colour vision has three sensors, and it reports every spectrum — a laser, a sunset, the whole sky — as one weighted sum across all of them. Violet light lands almost entirely on the blue-sensitive cone, the same cone blue light lands on, so to the eye a sky full of violet and a sky full of blue are nearly the same message. The brightest wavelength can wander; the integral can't follow it past blue, because past blue there is only one cone still listening.

So the sky isn't blue instead of violet. It is blue because the violet is there — scattered hard, ten parts to red's one — and then handed to an instrument that can't tell violet from blue and answers, every time, in blue.

The check — recomputed, not asserted

Every swatch above is integrated live from two formulas: a 5778 K blackbody for sunlight, and the published analytic fit to the eye's three CIE 1931 colour-matching curves. The verifier runs the same math headless and pins these numbers (research/why-isnt-the-sky-violet/verify.mjs, 5/5 green):

The colour engine is honest first: a flat, equal-energy spectrum returns white at (0.333, 0.334) — the known invariant — and a 6500 K blackbody returns (0.313, 0.324), right next to standard daylight D65. We validate the instrument before trusting its verdict.
The Rayleigh-scattered solar spectrum is genuinely brightest at the violet end: its power at 400 nm is 10.4× its power at 700 nm, falling monotonically across the visible band.
Yet its colour is blue: chromaticity (0.237, 0.237), dominant wavelength 477 nm — a clean blue, and 47 nm away from where the violet band even begins.
The naive "colour = brightest wavelength" answer points to the short-wavelength edge of vision (~380–400 nm, deep violet); the eye's answer for the very same light is sRGB(141, 179, 255) — the swatch you see. Worth noting: spectral violet lies outside what a screen can show, so even the "violet answer" can only be rendered as a blue-leaning purple. The colour the sky can't be is one your monitor can't draw either — the gamut and the eye agree.