Leonardo da Vinci tried to explain the sky's color as early as about 1500. 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, and in 1869 he found that bright light scattered off tiny particles looks faintly blue-tinted. Next, in the 1870s, came Lord Rayleigh, whose work is the subject of the pages that follow.

In 1871 Lord Rayleigh published two papers on the color and polarization of skylight, to put numbers on Tyndall's effect, and Rayleigh's 1871 explanation of the sky's blue is a famous example of applying dimensional analysis. 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: blue light, at about 400 nanometers, is scattered about ten times more than red light, at about 700 nanometers. In plain terms, a factor of about ten separates how strongly the two ends of the visible range are scattered.

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. Light scattered by these molecules travels in all directions, so a patch of sky far from the Sun still shines with blue light and gives diffuse sky radiation.

Tiny density fluctuations in a fluid 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 scattered light of clear skies produces their brightness and color, and in the fluid case the same word, scattering, is used for the blue coloration that tiny fluctuations produce.

Because shorter wavelengths scatter most strongly, there is a puzzle as to why the sky does not look violet, since 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. Human vision is less sensitive to violet wavelengths than to blue ones, and 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. A blue rather than violet sky needs several effects together: the scattering, how little violet sunlight holds, and how our eyes respond.

Rayleigh's model has a limit, and the limit is a matter of size. It 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 the effect 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, and 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.

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, and on Earth sunsets are red because the molecules in the air scatter or filter out the blue light. Blue skies and red sunsets come from the same scattering process, so the blue overhead and the red at the horizon are two results of one effect. 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.

The atmosphere thins with height and has no definite boundary with outer space, and the Kármán line at 100 kilometers is often used as a conventional edge of space. Half of the mass of the atmosphere lies in the lowest 5.5 kilometers, which is the lower troposphere. The Moon, by contrast, 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, and dust storms there are not rare. To our eyes, the sky on Mars would look hazy and red because of suspended dust, yet a NASA rover took a color picture of a sunset on Mars in which the sky around the setting Sun looked blue.

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, a gas made of three oxygen atoms (O3) that is mostly held in the stratosphere. Ozone there is made when ultraviolet light strikes ordinary oxygen, and the layer lies between about 9 and 30 miles above the ground and absorbs most of the Sun's ultraviolet radiation. The ozone layer formed about 500 million years ago, so the layer is about 500 million years old.

The ozone layer absorbs 97 to 99 percent of the Sun's medium-frequency ultraviolet light, and oxygen (O2) and ozone (O3) together absorb almost all radiation with wavelengths shorter than 300 nanometers. The total mass of ozone in the atmosphere is only about 3 billion metric tons, and the thickness of the ozone layer varies worldwide: it is generally thinner near the equator and thicker near the poles. In figures, then, the layer is thin in mass, uneven in thickness and nearly complete in its absorption of the shortest wavelengths. Those shortest wavelengths are the ones below 300 nanometers, a region that lies outside the 380 to 750 nanometers that an eye responds to.

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. The ozone behind the blue hour is the same gas whose discovery depended on missing radiation, and its absorption of red light is a different cause of blue from the scattering that colors the midday sky. At mid-latitudes the span is 20 to 30 minutes, near the equator it is shorter, and in the polar night it can stretch to hours.

The light of the sky is polarized, which a polarizing filter can show, and scattered blue light is polarized. Sky light is most strongly polarized at points 90 degrees from the Sun. Many insects, including bees, can sense the polarization of skylight. It has been suggested, controversially, that the Vikings used a polarization-sensing device to navigate by the sky, and the word controversially means that the suggestion is argued about and not settled. Rayleigh's 1871 papers were about the color and polarization of skylight, so polarization belongs to the same scattering story as the 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, which is a different process from the scattering that colors the sky of Earth. The sky itself is colored by scattering: the scattered light of clear skies produces their brightness and color, and the blue of the sky of Earth is a result of that scattering.

Return, then, to the sky overhead. Because shorter wavelengths scatter most strongly, there is a puzzle as to why the sky does not look violet, and the answer is that a blue rather than violet sky needs several effects together: the scattering, how little violet sunlight holds, and how our eyes respond. 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. All three effects act at once whenever someone looks up on a clear day, and together they produce the blue of the sky.

Words to know

• troposphere: lowest air layer
• opalescence: milky shimmer
• suspended: floating
• polarization: wave alignment
• exosphere: outermost air