2D Why Is the Sky Blue: Rayleigh Scattering

Sun Position

Sun elevation (time of day) 45°

Atmosphere

Particle density 1.0×

Sky State

Approx. time of day

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Path through atmosphere

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Scattered sky colour (zenith)

blue

Direct sunlight colour

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I(λ) ∝ 1 / λ⁴

How it works

Air molecules scatter short wavelengths (violet/blue) far more strongly than long ones (orange/red) — the scattered intensity follows I(λ) ∝ 1/λ⁴, so violet light (~400 nm) is scattered roughly 9× more than red (~700 nm). Looking anywhere at the daytime sky away from the sun, you're seeing this scattered light — mostly blue.

Sun elevation — near the horizon (sunrise/sunset) sunlight has to cross a much longer slant path through the atmosphere. Almost all the blue/violet gets scattered out of the direct beam along the way, so the sun itself — and the sky near it — turns orange and red. Overhead, the path is short, little gets removed, and the direct beam stays close to white.
Particle density — more air molecules per unit path means more scattering events. Turn it up and the whole effect intensifies: a deeper blue zenith and a more dramatic red sunset for the same sun angle (this is also why high humidity, dust or pollution near the horizon can deepen sunset colours).

Scattering intensity vs. wavelength — I(λ) ∝ 1/λ⁴