Because shorter wavelengths scatter most strongly, there is a puzzle as to why the sky does not look violet. If Rayleigh scattering were the only thing going on, the sky would look violet instead of blue. Violet is scattered even more strongly than blue, yet the sky does not look violet because sunlight contains less violet than blue. A rainbow shows that there is still a significant amount of violet and indigo light in sunlight beyond the blue, so lack of violet in sunlight is only part of the story. Many people think sunlight is a perfectly white color, but the Sun gives out more yellow light than any other color.

Human vision is less sensitive to violet wavelengths than to blue ones, which is another reason the sky looks blue and not violet. A typical human eye responds to wavelengths from about 380 to about 750 nanometers, though the edges are not sharp and vary from person to person. Our eyes have three kinds of color receptors, called cones, in the retina, and our brains mix the spectrum of skylight into the sky blue we see. In plain terms, the color is assembled by the eye and the brain from the spectrum of skylight that arrives. In numbers, the range an eye can respond to spans about 370 nanometers, from about 380 to about 750. A blue rather than violet sky needs several effects together: the scattering, how little violet sunlight holds, and how our eyes respond.

Isaac Newton used a prism to split sunlight into a spectrum, showing that white light is a mixture of colors, and each color in a rainbow corresponds to a different wavelength of electromagnetic radiation. Thomas Young was the first to measure the wavelengths of different colors of light, in 1802. The physicist John Tyndall took some of the first steps toward explaining why the sky is blue, in the 1800s. In 1869 Tyndall found that bright light scattered off tiny particles looks faintly blue-tinted, and the scattering of light by tiny particles can be shown by shining a beam of white light through a tank of water with a little milk or soap mixed in. Next came Lord Rayleigh, in the 1870s.

In 1871 Lord Rayleigh published two papers on the color and polarization of skylight, to put numbers on Tyndall's effect, and he worked out much of the scattering explanation in the 1870s. Rayleigh scattering, named after the 19th-century British physicist, is the scattering of light by particles much smaller than the wavelength of the light, such as individual air molecules. Under it the amount of light scattered is inversely proportional to the fourth power of its wavelength, so shorter waves scatter far more. Because of the fourth-power rule, blue light, at about 400 nanometers, is scattered about ten times more than red light, at about 700 nanometers, since blue has shorter waves. Light that has been scattered this way travels in all directions, so a patch of sky far from the Sun still shines with blue light and gives diffuse sky radiation.

If dust or water droplets were the main scatterers, sky color would vary with humidity or haze more than was actually observed. The air molecules that scatter sunlight are mostly nitrogen (N2) and oxygen (O2), and about 78 percent of the air is nitrogen and about 21 percent is oxygen, with the rest argon, carbon dioxide and other gases. Rayleigh used his calculation of scattering by air molecules as a further verification of Avogadro's number.

Tiny density fluctuations in a fluid also scatter light and produce a blue coloration known as critical opalescence. Marian Smoluchowski was the first to ascribe critical opalescence to large density fluctuations, and Einstein showed that the link between critical opalescence and Rayleigh scattering is quantitative.

The Rayleigh model stops working when particles grow larger than about 10 percent of the wavelength of the light. Mie scattering describes light scattered by particles whose size is comparable to the wavelength of the light, such as the droplets in a cloud, and it is named after the German physicist Gustav Mie, who developed the solution for the scattering of a light wave by a sphere. The dominant scattering processes in the atmosphere are Rayleigh scattering and Mie scattering. Mie scattering happens mostly in the lower atmosphere, where larger particles such as droplets and dust are more abundant. The greater the particle size, the more of the light is scattered in the forward direction. Clouds look white or grey because the droplets scatter in the Mie way, roughly equally at all wavelengths.

The ozone layer was discovered in 1913 by the French physicists Charles Fabry and Henri Buisson, who found that sunlight reaching the ground had no radiation below about 310 nanometers. The spectrum of the missing radiation matched only one known chemical, ozone. In other words, Fabry and Buisson read the sunlight that reached the ground and noticed what was absent from it: below about 310 nanometers there was no radiation at all, and the pattern of absence fit ozone and no other known chemical. Ozone is a gas made of three oxygen atoms (O3). Ozone in the stratosphere is made when ultraviolet light strikes ordinary oxygen. The ozone layer, in the stratosphere, absorbs most of the Sun's ultraviolet radiation, and it lies somewhere between about 9 and 30 miles above the ground.

The total mass of ozone in the atmosphere is only about 3 billion metric tons. The thickness of the ozone layer varies worldwide: it is generally thinner near the equator and thicker near the poles. Oxygen (O2) and ozone (O3) absorb almost all radiation with wavelengths shorter than 300 nanometers. In figures, the layer holds only about 3 billion metric tons, and it is thinner near the equator and thicker near the poles.

During the blue hour, the deep blue of the sky overhead comes from ozone in the upper atmosphere absorbing red light. The blue hour lasts about 20 to 30 minutes at mid-latitudes, can last hours in the polar night, and is shorter near the equator where the Sun sets steeply. In numbers, that is a span of 20 to 30 minutes in the middle latitudes and a span of hours in the polar night.

At sunrise and sunset the low Sun's light passes through a thicker layer of atmosphere, so more of the blue is scattered out of the beam. The reds and oranges of sunset are the longer wavelengths that remain after Rayleigh scattering has removed the shorter ones from the beam. Near the horizon the sky fades to a lighter blue or white, because closer to the horizon, light travels through more air and is scattered and re-scattered, mixing in white light and making the blue paler. When the Sun is low in the sky, its light has to go through more air to reach your eyes. Clouds low on the horizon at sunset can be lit red and orange by the sunlight that has been reddened on its long path, and if the air is polluted with small particles, natural or otherwise, the sunset will be more red. Never look straight at the Sun. Even dark sunglasses do not make it safe for your eyes.

Scattered blue light is polarized. The light of the sky is polarized, which a polarizing filter can show. Sky light is most strongly polarized at points 90 degrees from the Sun, which is to say a quarter of the way around the sky from it. Many insects, including bees, can sense the polarization of skylight. Rayleigh's 1871 papers were about the color and polarization of skylight, so polarization belongs to the same line of work as the blue itself, and the same scattered light that is blue is also polarized. To restate the facts that matter here: scattered blue light is polarized, the polarization is strongest 90 degrees from the Sun, and a polarizing filter or the eye of a bee can pick it up.

The Moon has only a very thin exosphere and no air to scatter sunlight, so its sky looks black even in the daytime. Mars has a thin atmosphere, with a surface pressure about 0.6 percent of Earth's, made up mostly of carbon dioxide, nitrogen and argon. Dust storms on Mars are not rare, and the dust changes the color of the Martian sky with the weather. To our eyes, the sky on Mars would look hazy and red because of suspended dust. By contrast, a NASA rover took a color picture of a sunset on Mars, and the sky around the setting Sun looked blue.

On Uranus, methane gas absorbs the red part of sunlight, giving the planet a blue-green color. The ocean is blue because water absorbs the red part of the light spectrum. In both cases the red part of the light is taken out by absorption.

Put the pieces together and the puzzle can be answered. Because shorter wavelengths scatter most strongly, there is a puzzle as to why the sky does not look violet. Violet is scattered even more strongly than blue, yet sunlight contains less violet than blue, and human vision is less sensitive to violet wavelengths than to blue ones. A blue rather than violet sky needs several effects together: the scattering, how little violet sunlight holds, and how our eyes respond. The blue sky is what the three effects produce together. In short, the blue of the sky is the sum of a rule about wavelengths, a fact about sunlight and a fact about the eye, and none of the three alone would give a blue sky.

Words to know

• scattering: bouncing everywhere
• wavelength: length of wave
• polarization: wave alignment
• opalescence: milky shimmer
• stratosphere: upper air layer
• suspended: floating