Scattering of Light

When light passes through a medium containing particles much smaller than its own wavelength -- such as the molecules of the gases making up the earth's atmosphere -- some of the light is absorbed and re-radiated by these particles in all directions, a phenomenon called scattering, quite distinct from ordinary refraction or reflection at a smooth surface. For particles very much smaller than the wavelength of light, the physicist Lord Rayleigh showed that the amount of light scattered is strongly wavelength-dependent, varying as $I_{\text{scattered}}\propto\frac{1}{\lambda^{4}},$ so that light of shorter wavelength is scattered very much more strongly than light of longer wavelength -- violet and blue light (shorter wavelength, roughly $400$-$450\ \text{nm}$) are scattered many times more strongly by air molecules than red and orange light (longer wavelength, roughly $600$-$700\ \text{nm}$) is. This single $1/\lambda^4$ law explains two everyday sights that, at first glance, seem to have nothing to do with each other. Looking at any part of a clear daytime sky away from the sun, an observer receives mostly sunlight that has been scattered sideways, out of the direct beam, by air molecules on its way through the atmosphere; since blue (and violet, to which the human eye is less sensitive) is scattered far more than red, orange or yellow, the sky one sees in every other direction appears blue. Looking directly at the sun near sunrise or sunset, by contrast, sunlight must travel an unusually long path through the dense lower atmosphere (compared with its much shorter, nearly-overhead path at noon), so that almost all of the shorter-wavelength blue and violet light is scattered away out of the direct line of sigh …