Why Is the Sky Blue (and the Sunset Red)? The Real Physics of Rayleigh Scattering

In 1869 the Irish physicist John Tyndall shone a beam of white light through a glass tube filled with a fine haze. Seen from the side, the haze glowed blue. Looked at end-on, the light that came straight through was tinged orange. Tyndall had made a small sky and a small sunset in his laboratory, and he suspected that the real ones worked the same way: tiny particles in the air scatter blue light more than red.

He was close. The full answer came from John William Strutt, Lord Rayleigh, in a paper of 1871. It also explains why sunsets are red, why clouds are white and why the sky on Mars is the colour of butterscotch.

Illustration: the same sunlight, scattered differently overhead and at the horizon.

Small particles prefer short waves

Sunlight contains every visible colour, from red at a wavelength of about 700 nanometres to violet at about 400. A prism or a raindrop separates them because each colour bends by a slightly different amount, but it doesn't create them.

Rayleigh worked out what happens when light meets particles much smaller than its own wavelength. The amount of light scattered sideways goes up with the inverse fourth power of the wavelength, written 1/λ⁴. Halve the wavelength and the scattering goes up sixteen times. Blue light at 450 nanometres and red at 700 differ by a factor of about 1.56 in wavelength, so the blue is scattered about 5.9 times more strongly.

Rayleigh at first assumed the scattering came from dust or droplets. In 1899 he showed that the molecules of air themselves, mostly nitrogen and oxygen, are enough. A decade later Albert Einstein and Marian Smoluchowski refined the picture: what scatters the light is the tiny, constantly changing unevenness in how densely the molecules are packed. Either way, the effect is that blue light coming from the sun is bounced around the sky in every direction, so whichever way you look, away from the sun, blue light reaches your eye from that patch of air.

Why not violet?

By the same rule, violet should be scattered even more than blue, and it is. The sky looks blue anyway for two reasons. Sunlight contains less violet than blue to begin with. And our eyes are poor at seeing violet: their sensitivity falls off steeply at the short end of the spectrum. Skylight is a broad mix of colours weighted towards blue and violet, and it stimulates the three kinds of colour-sensing cells in the eye in about the same proportions as a pale blue would. So that is what we see.

At sunset, light crosses so much air that most of the blue is scattered away before it reaches you. Photo: Nyall Engfield / Pexels

The same physics at sunset

At noon, sunlight comes down through a fairly short column of air. When the sun is on the horizon, its light travels sideways through the atmosphere, through roughly 38 times as much air as when it is overhead. Over that distance almost all of the blue and much of the green is scattered out of the beam. What reaches you directly is mostly orange and red. A red sunset is the blue being taken away, not red being added.

Dust, smoke and volcanic ash change the result. Particles from large eruptions can stay in the upper atmosphere for months; after Krakatoa erupted in 1883, sunsets around the world were so vivid that fire engines were called out in New York and Connecticut, because people thought the glow on the horizon was a fire. Wildfire smoke can turn the sun a deep red or orange in the middle of the day.

Cloud droplets are large enough to scatter all colours equally, so clouds look white. Photo: Nothing Ahead / Pexels

Clouds are white because their droplets, typically around 10 micrometres across, are much bigger than the wavelength of light. Rayleigh's rule no longer applies. Particles that size scatter all colours about equally, a process called Mie scattering after the German physicist Gustav Mie, and an even mix of all colours looks white. When clouds are thick enough to block much of the light behind them, they look grey from below.

Other skies

On Mars, the surface air pressure is less than one per cent of Earth's, so the thin air does little Rayleigh scattering. What colours the sky instead is fine dust, which absorbs blue light and gives the daytime sky its tan or butterscotch tint. At sunset the effect flips. The dust particles are just the right size to scatter blue light forward, close to the direction of the sun, so the sky right around the setting sun turns blue. NASA's Curiosity rover photographed this in Gale Crater in April 2015.

The colour of the sea is a separate question. Water reflects some of the blue sky, which is why a lake looks grey on a grey day. But water also absorbs red light slightly more than blue, an effect strong enough to give a deep pool of clean water its own blue colour, as Charles Braun and Sergei Smirnov explained in a 1993 paper. The sky does not get its colour from the ocean. If anything, it is the other way round.

Sources

1. J. W. Strutt (Lord Rayleigh), "On the light from the sky, its polarization and colour", Philosophical Magazine 41 (1871): 107–120. https://doi.org/10.1080/14786447108640452
2. NASA Space Place, "Why is the sky blue?". https://spaceplace.nasa.gov/blue-sky/en/
3. Rod Nave, "Blue sky and Rayleigh scattering", HyperPhysics, Georgia State University. http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html
4. NASA Jet Propulsion Laboratory, "Sunset in Mars' Gale Crater" (PIA19400, Curiosity rover, 2015). https://www.jpl.nasa.gov/images/pia19400-sunset-in-mars-gale-crater/
5. Charles L. Braun and Sergei N. Smirnov, "Why is water blue?", Journal of Chemical Education 70 (1993): 612. https://doi.org/10.1021/ed070p612