Why Is There No Purple in the Rainbow?

There is no purple in the rainbow because purple is not a wavelength of light. A rainbow is sunlight spread out in order of wavelength, from red at about 700 nanometres to violet at about 380, and violet is where it stops. Purple and magenta are what you see when red light and blue light reach your eye at the same time, and a rainbow never delivers them together, because it has just finished separating them. Purple lives in your brain, not in the spectrum.

• There is no purple in the rainbow because purple is not a wavelength of light.
• A rainbow runs from red at about 700 nanometres to violet at about 380, and stops.
• Purple and magenta are what your brain makes when red and blue light arrive together with no green.
• Violet is a real wavelength; purple is a mixture, and a spectrometer tells them apart instantly.

That is the answer. The details are where it gets interesting.

No, and the confusion is the whole story. Violet is a real wavelength, the shortest one you can see, sitting past blue at the end of the rainbow. Purple is a mixture: red plus blue, with no single wavelength of its own. They look similar to most people, which is why "purple" is used loosely for both, but a spectrometer can tell them apart instantly. Point it at the violet band of a rainbow and it reads one wavelength. Point it at a purple flower and it reads two peaks, one at the red end and one at the blue end, with a gap in between. Violet is on the map. Purple is a route between two places on the map.

Because beyond violet the wavelengths get shorter than your cones can respond to. That is ultraviolet, which bees can see and you cannot. A rainbow contains ultraviolet; it simply does not contain a colour for it, because colour is what your eye makes of a wavelength, and your eye makes nothing of that one. At the other end, past red, is infrared, which you feel as heat and also cannot see. The rainbow is not the whole spectrum. It is the slice of the spectrum your three cone types can report.

Because your brain does not measure wavelength. It compares the responses of three cone types, roughly tuned to long, medium and short wavelengths, and builds a colour from the ratios. When red light and blue light arrive together, the long cones and the short cones fire and the medium cones stay quiet. No single wavelength produces that pattern, so your brain has no rainbow colour to assign. It invents one. That invention is purple, and its most extreme version, where red and blue are balanced and green is fully absent, is magenta.

It is as real as any colour you experience, and it is the clearest case of a colour that does not exist as light. Magenta is what your brain produces for "red and blue, no green". Put it another way: magenta is the absence of green. That is why it matters so much in printing. Cyan, magenta and yellow are the three subtractive primaries because each one removes exactly one of the additive primaries from white light: cyan removes red, yellow removes blue, and magenta removes green. A colour that is defined by what it takes away is never going to appear in a rainbow, which is defined by what is present.

The three colours that cannot be mixed article explains the primaries in full.

Because the wheel is a map of perception and the spectrum is a map of physics. The spectrum is a straight line from red to violet with two loose ends. Your brain, though, sees red and violet as neighbours, because both are far from green and the red-green channel treats them alike. Newton noticed this and bent the line into a circle, inserting purple to close the gap. Every colour wheel since has done the same. The purples and magentas on the wheel between red and violet are the "non-spectral" colours: the ones that exist only where the two ends of the rainbow meet in your head.

Yes, by overlapping. Hold a magenta filter to the light and you are watching purple being manufactured: the filter removes green from white light and passes red and blue together, which your brain reads as magenta. Add a cyan filter and the red goes too, leaving blue. Add yellow instead and the blue goes, leaving red. A CMY Cube carries all three filters on one object, so you can turn it in a window and watch magenta, the colour that is not in the rainbow, appear and disappear as the faces overlap. It is the neatest demonstration of a non-spectral colour there is, and it fits in a pocket.

Nothing, because purple is not in it. The order of a rainbow is red, orange, yellow, green, blue, violet, and then ultraviolet, which has no colour. If you learned "indigo" between blue and violet, that is Newton's doing: he wanted seven colours to match the seven notes of the musical scale, and most people cannot actually pick indigo out as a separate band. Six is closer to what the eye reports. Purple was never one of them.

A rainbow is light sorted by wavelength, and it ends at violet. Purple and magenta are not wavelengths; they are what your brain builds when red and blue arrive together with no green, which a rainbow never provides. Violet is on the spectrum, purple is on the wheel, and magenta is the colour that exists only because green is missing. Hold a magenta filter to the light and you can watch it happen.

Make the colour that is not in the rainbow, and step into a world of colour and curiosity.