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Scatterina

Rayleigh Scattering / Why the Sky Is Blue Physics

\[I_s \propto \frac{1}{\lambda^4}\]
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Why is the sky blue? Scatterina is a nitrogen molecule in the air. Molecules much smaller than a wavelength scatter short-wavelength light far more strongly than long, in proportion to 1/λ⁴, so blue sunlight is sent across the sky while most red carries straight on. Lord Rayleigh explained this in 1871. This is a 3" pixel-art sticker from Pixelated Physics.

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The physics

Small particles and molecules scatter short wavelengths much more strongly, in proportion to one over wavelength to the fourth power. Blue light is scattered about 5.9 times more than red, which is why the sky looks blue.

Scatterina is a nitrogen molecule, two atoms and a triple bond, and white sunlight keeps walking into her.

A molecule is far smaller than a wavelength of light. Light shakes its electrons, and they re-radiate it in new directions. The power scattered this way goes as 1/λ⁴, so short wavelengths are scattered far more than long ones.

Blue at 450 nm is scattered (700/450)⁴ ≈ 5.9 times more than red at 700 nm. In the art she tosses six blue photons for every red one. Red is scattered too, just much less, so most of it carries straight on.

Lord Rayleigh worked this out in 1871. It is why the daytime sky is blue, and why the low sun, seen through a long path of air, looks red.

Blue gets tossed. Red goes through.

Equations

\[I_s \propto \frac{1}{\lambda^4}\]
\[\frac{I_s(450\,\mathrm{nm})}{I_s(700\,\mathrm{nm})} = \left(\frac{700}{450}\right)^4 \approx 5.9\]
SymbolMeaningUnit
\(I_s\) power scattered by a molecule much smaller than the wavelength \(\mathrm{W}\)
\(\lambda\) wavelength of the light \(\mathrm{m}\)

Sources

  1. Strutt (Lord Rayleigh) (1871) On the light from the sky, its polarization and colour, Phil. Mag. 41, 107
  2. Feynman Lectures on Physics Vol. I Ch. 32: Radiation Damping. Light Scattering

Source Strutt, J. W. (Lord Rayleigh) (1871). On the light from the sky, its polarization and colour. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 41, 107–120.doi.org/10.1080/14786447108640452

Field notes

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