Why the Sky Is Blue, and Why It Isn’t Violet

Violet scatters about twice as strongly as blue, so the sky ought to be violet; resolving that takes an eye and a spectrum.

“Shorter wavelengths scatter more.” That sentence is very nearly the entire content of the standard answer to why the sky is blue, and it is what NASA’s education pages, the observatory outreach sites, and most of the explainers written before this one offer. It is correct. It is also not an explanation, since it says nothing about why short wavelengths should scatter more, and nothing whatever about how much more. The “how much” is where the trouble starts. The law that governs it is Rayleigh scattering, the scattering of light by particles far smaller than the wavelength of the light itself. John William Strutt, Lord Rayleigh, worked it out in the 1870s, and it says that scattering rises as the inverse fourth power of the wavelength; an inverse fourth power is steep enough that violet light, at the short end of the visible band, scatters roughly twice as strongly as blue. By that reckoning the sky should be violet. It is not.

Why the sky is blue ranks among the most-asked why questions in English, which makes the thinness of the usual answer conspicuous. What follows earns the law instead of quoting it. The inverse-fourth-power dependence…