Light arriving at your eye is a curve — an amount of energy at every wavelength, an infinity of independent numbers. What reaches your brain is three. Three kinds of cone, each adding up the light it happens to be sensitive to, and everything you have ever seen is a point in that three-dimensional space. This is a catastrophic loss of information, and it is also the entire reason a screen with three coloured dots can convincingly show you a sunset.
The three cones are called L, M and S for long, medium and short, and they peak at 564, 534 and 420 nanometres. Look at how much the L and M curves overlap — they are barely different, which is why we are so much better at telling apart yellows and greens than blues. Each cone reports one number: the whole spectrum multiplied by its own curve and added up. Change the light source above and watch the spectrum change shape wildly while only three numbers come out the other end.
In 1931 a committee sat people in a booth and had them mix three lamps until the mixture matched a pure colour, for every wavelength across the spectrum. The averaged results are the colour matching functions, and they are still the definition of colour used by every camera, printer and display today. Plot them as a two-dimensional map and every colour a human can see falls inside one horseshoe. The curved edge is the pure wavelengths. The straight line closing the bottom is the interesting one: those colours are not in the rainbow. Press "red and blue together" above and watch the marker drop into that region — the tile will tell you that no wavelength anywhere gets within 0.21 of it. Magenta is not a kind of light. It is what your brain reports when the long and short cones are both driven hard and the middle one is not, and since every single wavelength that excites L also excites M (look at how those two curves overlap in section 1), nothing in the spectrum can ever produce that pattern. Magenta is a conclusion, not a colour of light.
Here is the payoff. On the left is the spectrum you chose. On the right is a completely different spectrum — three narrow peaks, like the ones inside your screen — whose weights have been solved so that all three cones report exactly the same numbers. The curves have almost nothing in common. The colours are identical, and not approximately: the two sets of tristimulus values below agree to four decimal places. Two lights that a spectrometer would call utterly different are, to you, the same colour. That is metamerism, and every screen you own depends on it completely.
Because colour is only three numbers, any three lights that are far enough apart can reach a whole volume of them by mixing — that is why three primaries work at all, and why a fourth would buy you almost nothing. But mixing can only ever reach inside the triangle joining your three primaries, and the horseshoe is curved. A triangle cannot fill a curve. The colours in the shaded region exist, you can see them, and no screen with three primaries has ever shown you one — which means the vivid cyan you remember from a real object has never once appeared on a display.
| colour space | red | green | blue | share of the horseshoe covered |
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About one man in twelve has a cone missing or shifted, almost always the L or the M — the two that overlap so heavily. With only two numbers instead of three, whole families of colours that used to be distinguishable collapse onto each other, and the lines below show exactly which ones: every colour along a confusion line becomes the same colour. This is not seeing in grey. It is seeing a two-dimensional slice of a three-dimensional space, and the person doing it has no way to notice anything is missing.
The colour matching functions are the actual CIE 1931 2-degree standard observer, tabulated at 10 nm from 380 to 780 nm, and the page checks itself against two independent published facts. An equal-energy spectrum — illuminant E — must land exactly at the centre of the diagram, and this table puts it at x = 0.333381, y = 0.333448, which is within 0.00012 of one third; the residual is the 10 nm sampling and nothing else. Standard daylight D65, computed from its own published spectrum, comes out at (0.3127, 0.3291) against the published (0.3127, 0.3290). Individual spectral colours agree with the published chromaticities to four decimal places at every tabulated wavelength — 700 nm at (0.7347, 0.2653), 520 nm at (0.0743, 0.8338). The metamer in section 3 is solved by inverting a genuine 3x3 system, not fitted, which is why the two colours agree exactly rather than closely.
One result worth stating plainly because it is easy to miss: the colours along the straight bottom edge of the horseshoe have no wavelength at all. The lab checks this rather than asserting it — for the two-peak red-and-blue spectrum the nearest point on the entire spectral locus is 0.211 away in chromaticity, which is most of the width of the diagram, and the cone shares come out 38.2 / 29.0 / 32.8 with the middle cone lowest of the three despite sitting between the other two in wavelength. That pattern is unreachable by any pure light, which is exactly why magenta is missing from every rainbow you have ever seen.
The cone curves are a model. Measuring the sensitivity of a single human cone is very hard, so section 1 uses the Govardovskii visual-pigment template with peaks set to the accepted 564, 534 and 420 nm and then sampled onto the same 10 nm grid as the rest of the page, so the drawn curves crest at the nearest tabulated point rather than exactly at the peak — the shape is a well-tested formula for what a retinal pigment does, not a direct measurement of your eye, and it omits the filtering that the lens and the yellow macular pigment do before light ever reaches a cone. The dichromacy simulation in section 5 uses the Vienot, Brettel and Mollon projection, which is the standard method, but no simulation can tell you what another person experiences — it can only tell you which colours they cannot tell apart, and that is a much narrower claim. Three more things this page cannot show you honestly. The out-of-gamut colours in section 4 are being displayed on your screen, so by definition you are not seeing them; they are drawn as the nearest colour your display can manage. Colour appearance depends enormously on surroundings, adaptation and brightness, none of which is here — the same chromaticity looks brown in one context and orange in another. And rod vision, which takes over in the dark and is entirely colourless, is left out completely.