Why the sky is blue (and sunsets are red)

Every child asks it and few adults can answer: if air is transparent, where does all that blue above us come from? The answer is not in air somehow "painted" blue — it is in what individual molecules do to the light that hits them. The figure below has two views: first look at a single molecule, then lower the sun towards the horizon and watch the same physics turn the blue of noon into the red of sunset.

A molecule like a microscopic antenna

A nitrogen or oxygen molecule is a few hundred times smaller than a wave of visible light. As the wave passes, its electric field shakes the molecule’s electrons — and a shaken charge becomes a transmitter itself, re-radiating a wave in all directions. That is Rayleigh scattering. What matters is how strongly: short waves shake the electrons faster, and the radiated power grows with the fourth power of the frequency. In the MOLECULE view, slide the wavelength and compare the rings: violet and blue scatter several times more strongly than red.

Blue from everywhere, the sun from one direction

Look at any patch of sky away from the sun. The light coming from there is sunlight that collided with air molecules along the way and got knocked off course — straight into your eye. And since it is mostly the short waves that get knocked, the whole ceiling of the world glows blue. The sun itself you see in the light that made it through unscattered: that is why at noon its disc is only a touch warmer than true white. Astronauts, who have no atmosphere above them, see a black sky at high noon.

Sunset: the same physics, a longer path

In the evening neither the sun nor the air changes — the geometry does. When the sun sits low, its rays enter the atmosphere at a slant and must punch through dozens of times more air than at noon. Over such a long haul, scattering has time to sweep nearly all the blue and green out of the beam — what reaches your eye is whatever scatters least: orange and red. In the SKY view, lower the sun and watch the air-mass readout: at the horizon light crosses about 38 “atmospheres”, and only a trace of the blue survives.

The blue of the sky and the red of a sunset are one phenomenon seen from two sides.

The same arithmetic explains why clouds are white: water droplets in a cloud are much larger than a light wave, so they scatter all colours almost equally (that is Mie scattering, not Rayleigh) — and mixed colours make white. And why cigarette smoke looks bluish while its particles are tiny, then turns white as they clump together. Obstacle size versus wavelength — that is the whole criterion.

A simplificationWe compute single Rayleigh scattering in clean air: we ignore aerosols and dust (Mie scattering, which amplifies and whitens sunset glows), ozone absorption (which helps the sky after dusk) and multiple scattering. Air mass follows the Kasten–Young formula, and colours are mixed from six spectral bands roughly weighted by eye sensitivity. The heart of it — the fourth power and the path length — is untouched.