Dear Deborah,

Thanks for your message and question about sky colours. You remind me that I must finish my webpages about the sky!

Your question is a rich and fascinating one and it has interested me for a long time - ever since it was incorrectly explained to me at school. The basic answer is pretty straighforward but there are several subtleties which are not widely known.

You are right that the clear sky is blue because of scattering. The scattering is mostly by air molecules (nitrogen, oxygen etc.) but also by larger particles such as aerosols, dust and general crud. The molecular scattering was first investigated and explained by Lord Rayleigh - the English physicist - and therefore takes his name. The molecules are much smaller than the wavelength of light and the scattering efficiency depends on the inverse fourth power of the wavelength: so S(lambda) ~ (lambda)^-4 (see the Feynman Lectures, Vol. 1, 32-5). This accounts for the clear sky being much bluer than direct sunlight. In a clear daytime sky, all the atmosphere we see is illuminated by the sun and so the light from the sky has all (or almost all) been Rayleigh scattered. Some of the light, however, is scattered by the larger particles and aerosols which - because they are closer in size to the wavelength of light - scatter more-or-less independently of colour and so appear as white or grey. Clouds, of course, are water droplets and scatter very efficiently but independently of colour - and so are (kind of) white.

Incidentally, since scattering is so much more efficient from particles which are close in size to the wavelength, the same fraction of water in a volume of air scatters much more light as a cloud than as water vapour (a gas and so much smaller than the wavelength) or as raindrops (much larger than the wavelength). This is why you can see through damp air and through rain - but not through cloud!

Ok, but so far I've told you nothing new. The trick for generating the whole range of "twilight colours" is that light gets scattered towards you - which is blue - and also AWAY from you - which means that the blue light gets taken away. When the sun is low in the sky, the light which reaches you directly has to travel through a long pathlength of atmosphere and so most of the blue light gets scattered away from you (to make the blue sky). What remains is yellow or red - depending on the depth of atmosphere traversed. Mathematically, the light you see from the sun (F_sun) is attenuated by the intervening Rayleigh scattering optical depth so that:

F_observed = F_sun * exp[-constant*pathlength/lambda^4]

When the Sun is low in the sky or after it has set, parts of the atmosphere are illuminated directly by it and other parts are in shadow. The parts which are in shadow between you and the Sun or between you and the illuminated atmosphere only scatter light OUT OF the beam - making it redder. The delicate balance between the amount of light scattered into- and out of- the beam entering your eye produces the whole beautiful range of twilight colours - including apple green! I have drawn a diagram (below) which I hope illustrates this. The variations amongst different twilights depend mostly on the aerosol and dust content of the atmosphere.

The black curve represents the spectrum of the Sun, the white one shows the Rayleigh scattered Sun (ie, the blue sky) and the lower pink ones the blue sky which has been attenuated by different pathlengths of shadowed atmosphere - producing the gentle gradation between blue, through a pale apple green, yellow, orange and finally red.

I have a lovely model of this in the form of a small fish made of glass which contains very small metal particles (a metal vapour) - I call him Rayleigh's Fish. If I shine white light on him, he scatters light in such a way as to produce the whole range of twilight colours. The blue light gets scattered first leaving the longer wavelengths to be scattered later. In this photo, the beam of light is shone through his eye...

Well, I hope this has explained the basic mechanism. Before I finish, let me suggest that you look at a wonderful classic book called "Light and Colour in the Open Air" by M. Minnaert (DOVER, ISBN 0-486-20196). Minnaert was a famous Flemish Solar physicist who wrote this in Dutch in the '30s and the book was translated into English in several editions. There is a recent edition with modern photographs called "Light and Color in the Outdoors" published by Springer-Verlag (ISBN 0-387-94413-3).

One of the subtleties I referred to in the beginning concerns the effect of ozone on the colour of the sky. Ozone has a weak absorption band in the orange (as well as the very strong one in the UV which protects us from sunburn). This orange band has no effect when the sun is high in the sky. At sunset, however, when the light has to travel tangentially through a great thickness of atmosphere, the absorption of the orange light makes the zenith sky much bluer than can be accounted for by Rayleigh scattering alone. Water vapour plays a role in this as well.

The other concerns the polarization produced by scattering - but that is another story... You could look at the note about the polarizer on my homepage to see some pictures of what this looks like.

Best wishes, Bob Fosbury (astronomer working on the Hubble Space Telescope project)