by PhilipJ on 18 May 2007
Things are never as simple as they seem, and as Chad pointed out in the comments, there’s more to the story than either of us mentioned to begin with.
The intensity of Rayleigh scattered light does indeed go as 1/λ4, and the human eye does have a peak in sensitivity in the blue, but the incoming solar radiation is also peaked in the blue. Here’s some data from MODIS, a spectroradiometer operated by NASA, where we’re particularly interested in the spectrum as it appears at sea level:
(Image from Wikipedia)
If we take the ratio of the scattering cross section for blue (say λ = 450 nm) and purple (λ = 400 nm) light I get value of 0.68 (ignoring dispersion) — the blue light will scatter less than the purple. If we compare the intensities of the blue and purple sections of the spectrum at sea level, the ratio is about 1.5 — this will make up for the slightly smaller scattering cross section in the blue. From both these values, there should be a little more blue than violet reaching our eyes from the sun. And as our eyes are more sensitive in the blue than in the violet to begin with (see the graph in the last post), the sky will appear blue.
It isn’t quite as simple as eye physiology or Rayleigh scattering. Perhaps not surprisingly, the Sun is important too.