Why the empty-looking air looks blue

Light is energy that travels. One accurate way to picture it for this question is as a wave, like a ripple, except the ripple is in electric and magnetic fields rather than in water. The distance from one peak to the next is the wavelength. Shorter wavelengths look violet and blue. Longer ones look orange and red. The sun sends a spread of wavelengths; together they look white. A prism — a triangular piece of glass — can fan that mix into a rainbow because each wavelength bends a different amount. The sky question is: which part of that mix gets steered toward your eye when you look at 'empty' air?

Air is not empty; it is molecules of nitrogen and oxygen, far smaller than the wavelength of visible light. When the oscillating field of a light wave hits such a molecule, the charges in the molecule jiggle and send out a new ripple. Sending light in a new direction this way is scattering. It is not the same as reflection off a mirror (which needs a large, smooth surface) and not the same as absorption (which is light energy staying in the material as heat). A little of each sunbeam is peeled off and sent sideways. Without scattering, looking away from the sun would show black sky, as it does on the Moon, which has no air.

This specific kind of scattering by very small particles is Rayleigh scattering, named after the person who worked out the rule. The rule is steep: if one wavelength is twice another, it scatters about sixteen times less (two to the fourth power is sixteen). Blue light has a shorter wavelength than red, so air peels blue out of the sunbeam much more eagerly. Violet is shorter still, so it scatters even more — but sunlight contains less violet than blue, and human eyes are less sensitive to violet, so the mix that reaches you from the side looks blue rather than purple. The leftover beam, heading straight toward someone looking near the sun, is missing some of its blue. That is why the sun itself looks slightly yellow at noon, and why sunsets go orange and red: the path through air is longer, more blue has been scattered away, and the remaining light is the long wavelengths.

If every scatterer in the air behaved like a tiny molecule, clouds would be blue too. They are not. A cloud is made of droplets — small but, compared with a molecule, huge. Scattering from objects around the size of the wavelength, or larger, does not follow the fourth-power rule. It is closer to equal for all visible colors, a regime often called Mie scattering. White in, white out. A thick cloud looks gray only because less light makes it through, not because the drops prefer a color. This contrast is the test of the theory: same sunlight, different scatterer size, different color. Haze and smoke can shift the sky toward white or brown for the same reason — the particles are larger than molecules.