The sky is not violet because the colour we see is decided by our eyes as well as by the air. Air molecules scatter short waves of light far more strongly than long ones, and violet is the shortest colour we can see: violet light at 400 nanometres is scattered about nine times as strongly as red at 700, and about 1.6 times as strongly as blue at 450. Skylight really does contain a great deal of violet. But the Sun sends less violet than blue to begin with, the air removes a little, and above all the three kinds of cone cell in a human eye respond to that whole mixture exactly as they would to pale blue.
That answer is recent. The physics behind it is a century and a half old, and it began with a glass tube.
Two enigmas and an artificial sky
For a long time the leading idea was that skylight was reflected. Lord Rayleigh later wrote that “by many physicists, from Newton downwards”, the light of the sky had been supposed to be reflected from thin plates, its colour the blue of the first order in Newton’s scale. Rudolf Clausius had built a whole theory on it: the air, he suggested, held tiny water bubbles whose thin films reflected blue, as a soap film does.
In 1869 the Irish physicist John Tyndall, professor at the Royal Institution in London, took the problem on. A letter from Sir John Herschel had pushed him to it. The blue colour of the sky and the polarisation of skylight, he wrote, “constitute, in the opinion of our most eminent authorities, the two great standing enigmas of meteorology.”
His apparatus was “a glass tube about a yard in length”, filled with a very thin vapour and lit along its length by the condensed beam of an electric lamp. The light broke the vapour down, and particles formed that he could keep to “but a small fraction of the length of a wave of violet light”. Whenever the vapour was thin enough, the first thing to appear was a blue cloud. Seen from the side its light was polarised, most strongly at right angles to the beam, just like the light of the sky. Tyndall called it an artificial sky.
Never, even in the skies of the Alps, have I seen a richer or a purer blue than that attainable by a suitable disposition of the light falling upon the precipitated vapour. — John Tyndall, Proceedings of the Royal Society, 1869
He could make the blue. He could not say why tiny particles should prefer it.
Rayleigh scattering and the inverse fourth power
The explanation came in February 1871 from John William Strutt, then twenty-eight, later the third Baron Rayleigh, in a paper in the Philosophical Magazine titled “On the light from the sky, its polarization and colour”.
His key step was an argument from dimensions. For a particle much smaller than the wavelength, the ratio of scattered to incoming wave can depend only on the particle’s volume, the distance and the wavelength. The speed of light cannot appear, because nothing else in the problem involves time. A volume divided by a distance leaves an area, and the only area left to divide by is the wavelength squared. Square the wave to get its brightness, and Strutt had his law: the intensity of the scattered light varies “as the inverse fourth power” of the wavelength.
Halve the wavelength and the scattering grows sixteen times. The video animates this step with the units cancelling one by one.
He tested it on the sky itself. Comparing blue light from near the zenith with sunlight diffused through white paper, he found the blue-green part of the spectrum (the line F) more than three times as strong, relative to the red line C, as in the sunlight, close to his theory. “I was not prepared for so great a difference as the observations show,” he admitted. The old thin-plate idea predicts a law of one over the wavelength squared; the sky, he found, agreed far better with the fourth power.
One question remained: what were the particles? Strutt began, like Tyndall, by assuming suspended matter. In 1873 James Clerk Maxwell wrote to him asking him to “stick the data into your formula” and see what it said about the size of air molecules. In 1899 Rayleigh answered in print: “even in the absence of foreign particles we should still have a blue sky.” The molecules of the air are enough. Turning the argument round, the clearness of the air told him there must be at least 7 × 10¹⁸ molecules in every cubic centimetre. The modern value, at 0 °C and normal pressure, is about 2.7 × 10¹⁹.
So why isn’t the sky violet?
The fourth-power law favours violet over blue, so the answer has to come from somewhere else. It has three parts, and they are not equally important.
The Sun. Sunlight is not an even mix. The Sun shines roughly like a body at about 5,800 K, brightest near blue-green, with less violet than blue to begin with. But the fourth-power law more than makes up for that: in the simple theory, scattered skylight keeps getting brighter all the way into the violet. As the physicist Glenn Smith put it in 2005, from these considerations alone “we could equally well say that the sky is violet.”
The air. Measured skylight carries less of the shortest wavelengths than the simple theory predicts. Ozone high in the atmosphere absorbs some light, but a 2023 calculation found that with the Sun high it changes the colour of the sky only by a few per cent. It is not the main answer.
The eye. This is the decisive part. Colour is a sensation, not a property of the light; Newton wrote that “the Rays to speak properly are not coloured”. We see colour with three kinds of cone cell, most sensitive near 570, 543 and 442 nanometres. The lens and a yellow layer over the centre of the retina absorb short wavelengths, and our eyes respond only weakly to violet. Smith worked the numbers through: the cones respond to the whole spread of skylight exactly as they would to pure blue light of about 474 nanometres mixed with white light. That is an unsaturated, pale blue, which is precisely the colour of a clear sky.
Why sunsets are red, and why the sky above stays blue
The same law explains the sunset. Rayleigh showed in 1871 that light passing through more and more of a scattering medium “tends to become yellow and finally red”, and noted “how little of the violet light remains when the red is still in nearly its original force”. When the Sun is on the horizon, its light crosses about 38 times as much air as when it is straight overhead. Along that path the short waves are scattered out of the beam, off to colour someone else’s sky, and what reaches you directly is orange and red. Tyndall knew the effect from the laboratory: in Ernst Brücke’s experiment, resin finely dispersed in water looks bluish from the side, yellowish when you look through it, and turns orange or red as the particles grow more numerous.
There is one last twist. At sunset the sky straight above you stays blue, but not only because of scattering. In 1953 Edward Hulburt estimated that, with the Sun on the horizon, absorption by ozone, which removes orange and yellow light, provides about two-thirds of the zenith’s blue. A 2023 calculation confirmed his estimate “with remarkably good agreement”.
So the sky is blue because air molecules scatter short waves by the fourth power. It is not violet because of the Sun’s spectrum, the air and, above all, our eyes. And the sunset is red because the long path strips the blue away. And that’s how we found out.
