Why the sky is blue, sunsets are red, and clouds are white: a short tour of light scattering

It is one of the first science questions children ask, and one of the most satisfying to answer properly: why is the sky blue? The short answer is "scattering," but the full story explains far more than one colour. The same physics tells us why sunsets glow orange, why clouds are white rather than blue, why the sky on Mars looks different, and why a pair of polarized sunglasses can make part of the sky look darker than the rest. Sunlight is a mixture White sunlight contains a broad spread of wavelengths. Visible light runs roughly from about 400 nanometres (violet) to about 700 nanometres (red), with blue, green and yellow in between. A prism or a rainbow separates these, but normally they arrive together and our eyes read the mixture as white or slightly yellowish. When that light enters the atmosphere, most of it travels straight to the ground. A fraction, however, interacts with the gas molecules of the air, mostly nitrogen and oxygen, and is redirected in new directions. That redirected light is what fills the daytime sky. If there were no atmosphere, as on the Moon, the sky would be black even at noon, with the Sun a blazing disc against darkness. Rayleigh scattering: small particles prefer short waves Air molecules are far smaller than the wavelength of visible light. In that situation the light's oscillating electric field makes the electrons in each molecule oscillate, and the molecule re-radiates light in many directions. Lord Rayleigh worked out the mathematics of this in the late nineteenth century, and the key result is striking: the amount of scattering rises steeply as wavelength gets shorter, in proportion to one over the wavelength to the fourth power. That fourth power matters a great deal. Compare blue light near 450 nanometres with red light near 700 nanometres. The ratio of wavelengths is about 1.56, and raising that to the fourth power gives nearly 6. So blue light is scattered roughly five to six times more strongly than red. Look at any part of the sky away from the Sun and you are mostly seeing this scattered short-wavelength light coming at you from every direction. So why not violet? If shorter wavelengths scatter more, violet should win, and in a sense some of the scattered light really is violet. Several things tip our perception toward blue. The Sun's output is lower at the violet end than in the blue-green, so there is less violet to begin with. Some of the shortest wavelengths are absorbed high in the atmosphere. Most importantly, human eyes are not very sensitive to violet. Our colour vision relies on three types of cone cells, and the combined signal produced by the actual mixture of scattered light is interpreted by the brain as a pale sky blue rather than purple. The colour of the sky is therefore partly physics and partly biology. Sunsets: the long way through the air When the Sun is high, its light crosses a relatively thin slice of atmosphere. Near sunrise or sunset the light travels a much longer, slanting path. Along the way, blue light is scattered out of the direct beam again and again, so what remains in the beam by the time it reaches you is weighted toward yellow, orange and red. The Sun itself looks redder, and clouds lit from below by that filtered light can turn brilliant pink and crimson. Dust, smoke and volcanic aerosols can make sunsets more vivid or more muted depending on particle size and amount. That is why unusually colourful twilights are sometimes reported after large volcanic eruptions or during wildfire seasons. Clouds: when particles get big Cloud droplets are much larger than air molecules, typically comparable to or bigger than the wavelength of visible light. In that size range the simple Rayleigh law no longer applies. Scattering is described instead by a more general theory associated with Gustav Mie, and for particles of this size all visible wavelengths are scattered by similar amounts. The result is white. Thick clouds look grey or dark from below not because the droplets change colour but because so much light has been scattered away before it can reach the cloud base. The same idea explains why milk is white, why fog is white, and why a glass of water with a few drops of milk can look faintly bluish from the side and orange when you look through it at a light. That simple kitchen demonstration is a miniature sky and sunset in a glass. The sky on other worlds Planetary skies depend on what is floating in them. On Mars the atmosphere is thin, and fine reddish dust suspended in it dominates the daytime colour, giving a butterscotch or tan sky. Images from Mars rovers have shown something that surprises many people: Martian sunsets can look bluish near the Sun, because the dust particles there scatter blue light forward, toward the observer, more effectively than red. The physics is the same everywhere; only the ingredients change. A bonus: the sky is polarized Scattered skylight is also partly polarized. The effect is strongest in a band of sky about ninety degrees away from the Sun. If you wear polarized sunglasses and slowly tilt your head while looking at different parts of a clear sky, you can see that band darken and brighten. Many insects, including honeybees, are known to use sky polarization patterns to help them navigate. Something to discuss Rayleigh's fourth-power law turns a simple question into a window on molecules, eyes and other planets. Here is a question for the forum: if you could stand on a planet with a much thicker atmosphere than Earth's, made of the same gases, what colour do you think its midday sky and its sunsets would be, and why? I would love to see people reason it through, and anyone who has tried the milk-in-water experiment is welcome to share what they saw.