Rayleigh Scattering
Why the sky is blue. Builds on Traveling EM Waves.
You’re explaining to a friend why the sky is blue. They say, ‘It’s because the ocean reflects blue light upward.’ You know the real answer involves scattering of sunlight by air molecules.
By what factor does blue light (λ ≈ 450 nm) scatter more strongly than red light (λ ≈ 650 nm) in the atmosphere?
About 5.5 times more! Rayleigh scattering intensity goes as 1/λ⁴ — the fourth power of wavelength. Blue light (450 nm) scatters (650/450)⁴ ≈ 5.5× more than red light (650 nm). That steep dependence is why the sky is so vividly blue, not just slightly tinted. And it’s why sunsets are red — the blue has been scattered away during the long path through the atmosphere!
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Send white light through an atmosphere of molecules. Watch blue rays scatter in all directions while red passes straight through. Adjust the path length to see the transition from blue sky (short path) to red sunset (long path).
I ∝ (1/λ⁴) · (1 + cos²θ)
The 1/λ⁴ dependence is extraordinarily steep. Halving the wavelength increases scattering by 16×! This is why UV rays scatter even more than blue — and why Rayleigh scattering is negligible for radio waves.
At sunset, sunlight traverses hundreds of km of atmosphere. Blue and green scatter away along this long path, leaving reds and oranges. Volcanic ash and pollution add extra scattering, making even redder sunsets.
Distant mountains appear blue because of Rayleigh-scattered blue light from the air between you and the mountain. The Blue Mountains of Australia and Blue Ridge Mountains are named for this effect.
The Moon has no atmosphere, so there’s no Rayleigh scattering. The sky is black even during ‘daytime.’ Stars are visible next to the blazing Sun. This proves the blue sky is an atmospheric phenomenon.
Mars’ thin atmosphere has fine dust that scatters long wavelengths more efficiently (Mie scattering). This reverses Earth’s effect: Martian skies are butterscotch, but sunsets are eerily blue!
“The blue sky is painted by the fourth power of wavelength. Blue scatters 5× more than red — and that one fact explains both noon’s blue sky and sunset’s red glow.”
Scattering Lab
Simulate sunlight scattering through an atmosphere. Control the path length, atmospheric density, and wavelength mix. See how the sky color changes from overhead (blue) to horizon (white/reddish) to sunset (deep red).
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Start with the sun directly overhead and observe the blue sky. Now lower the sun toward the horizon and watch the sky color shift from blue through orange to deep red. Toggle individual wavelengths on/off to see how each one scatters differently. Try an atmosphere of larger particles (Mie scattering) to see why clouds are white — all colors scatter equally!
Rayleigh scattering (1/λ⁴) for particles much smaller than the wavelength produces blue skies. Mie scattering (all wavelengths equal) for particles comparable to the wavelength produces white clouds. The size of the scatterer relative to the wavelength determines the color.