Recently I found this article answering the famous question 'Why is the sky blue' a bit different and deeper than I read before. In physics the usual explanation is that the Rayleigh scattering is inversely proportional to the fourth power of the frequency of the electromagnetic waves. This means that light of shorter wavelengths (like blue and violet) will be scattered much stronger in the atmosphere than light of longer wavelengths (like red). Therefore looking at the sky, away from the sun, as one sees only scattered light, we should see mainly light of shorter wavelengths. But then, why does the sky look blue and not violet?
The author of this paper goes one step further and adds the human color vision system with the three different color receptors (cones) to the picture. Due to this restriction to three types, there is the possibility for metamers, i.e. different mixes of light frequencies leading to the same color as perceived by the human eye. An example is the mixing of red and green light resulting in a perceived yellow exactly like the single frequency yellow light.
Armed with that background, he tries to identify a simple frequency spectrum which will be perceived the same as the frequency spectrum resulting from the sun and Rayleigh scattering. As model he adds a very narrow frequency range to a background of white light of all frequencies. Fitting the frequency of the narrow band to result in the same perceived color, one gets a background of white light with a narrow blue frequency range - corresponding to unsaturated blue. Ergo, we see the sky as blue not violet!
Nice paper and very readable!
For me, I recognized another important thing: one usually says that all colors are in the rainbow - but this is not true! Due to the fact that there are three different types of color receptors, a small frequency range will always produce some special combination of responses from the three receptor types - but not all possible combinations. For example: with a small frequency range, one cannot excite the low and the high frequency receptors without the medium frequency receptor.
But with a suitable mixture of various light frequencies I can get any combination of responses from the three types. I.e. there are many more perceived colors than the rainbow contains!
Corollary: for color blind people with only two types of color receptors the rainbow indeed contains all possible perceived colors.
Smith, G.S. 2005. Human color vision and the unsaturated blue color of the daytime sky. American Journal of Physics 73(July):590-597. Abstract available at http://dx.doi.org/10.1119/1.1858479.