Why is the sky blue, and sunsets red?

With the Sun 40° above the horizon, its light crosses 1.6 times as much air as it would straight overhead, and the sky is a deep, clean blue. Drag that number, or the Sun itself, down to the horizon and watch what Nib does to the sky.

Air is clear, so the colour has to come from what the air does to sunlight. Sunlight is a mix of every colour. Before you read on: which colour does air bounce around the most?

Violet. Air scatters violet light even more than blue. Hold on to that puzzle: we will come back to why the sky is not violet.

What does air do to a beam of light?

Sunlight is a wave, and each colour has its own wavelength: about 700 nanometres for red, 450 for blue, 400 for violet. The molecules of air are a thousand times smaller than that. When a wave washes over something so small, the molecule is shaken and sends a little of the light off in a new direction. That is scattering, and Lord Rayleigh worked out in 1871 that it depends steeply on the wavelength: halve the wavelength and the scattering grows sixteen times.²

Light of 450 nm (blue) is scattered 5.9 times as much as red light of 700 nm, and 2.2 times as much as green of 550. Drag the wavelength and watch the scattered rays.

So why isn’t the sky violet?

Because of what sunlight holds, and how eyes work. Sunlight has less violet in it than blue, but scattering favours violet so strongly that the sky’s light, multiplied out colour by colour, still keeps rising all the way to the violet end. The answer is your eyes, which don’t read a spectrum’s peak. They have three kinds of colour sensor, and the sky’s mixture (violet, a lot of blue, plenty of green, a little red) lands on them as a pale, slightly whitish blue: the colour we call sky blue.⁵

Why are sunsets red?

At noon, sunlight comes down through the air on a short, steep path. Near the horizon it comes in sideways, skimming through the atmosphere for hundreds of kilometres. Right at the horizon the path holds about 38 times as much air as the path straight down.⁴ Along that path, the blue is scattered out of the beam again and again, off to light up someone else’s sky. By the time the beam reaches you, mostly yellow, orange and red are left.

At 40°, the beam crosses 1.6 air masses and keeps 71% of its blue: the Sun looks white. The same scattering that steals the blue from a setting Sun paints the sky behind it, which is why a sunset sky glows orange low down. Scattering alone would turn the whole sky orange, as it does in Nib’s drawing; the real sky overhead stays blue into dusk because ozone, high up, soaks up orange light.⁸

Why are clouds white?

Rayleigh’s rule is for particles far smaller than the wavelength, like molecules. Cloud droplets are about ten micrometres across, fifteen times longer than a wave of red light, and they scatter every colour about equally. Scatter every colour equally and you get white.

Make the particles molecules: the scattered light is deep blue, like a clear sky. Drag toward droplets and watch the blue wash out to haze, then white. (This is a simple stand-in for the full theory, Mie scattering, which also explains why haze and smog look milky.)

Wait, but then…

On Mars the daytime sky is a dusty butterscotch, and the sunsets are blue. NASA’s Curiosity rover photographed one in Gale Crater on 15 April 2015.⁷ Mars has almost no air to scatter light, but it has plenty of very fine dust. What would the dust have to do to blue light, compared with red, to put a blue glow right around a setting Sun?

Try it yourself

Each task ticks itself off when the page above shows it.

1. Set the Sun low enough that it turns orange or red.Below about 5°, the beam crosses more than ten times the air of the overhead path, and most of its blue has been scattered out.
2. Find a colour that air scatters at least twice as strongly as green light of 550 nm.Scattering goes as 1/λ⁴, so twice green’s needs (550/λ)⁴ ≥ 2: any wavelength below about 462 nm, which is blue to violet.
3. Make the scattered light white.Particles much bigger than the wavelength scatter every colour about equally: clouds, fog, milk.
4. In your own words: why is the sky red at sunset but blue at noon?

So the sky is blue because air scatters short waves of light far more than long ones and sends blue to your eyes from everywhere, and sunsets are red because that same scattering, over a long, low path, has taken the blue away before the light arrives.