A clear cloudless day-time sky is blue because molecules in the air scatter blue light from the sun more than they scatter red light. When we look towards the sun at sunset, we see red and orange colours because the blue light has been scattered out and away from the line of sight.
The white light from the sun is a mixture of all colours of the rainbow. This was demonstrated by Isaac Newton, who used a prism to separate the different colours and so form a spectrum. The colours of light are distinguished by their different wavelengths. The visible part of the spectrum ranges from red light with a wavelength of about 720 nm, to violet with a wavelength of about 380 nm, with orange, yellow, green, blue and indigo between. The three different types of colour receptors in the retina of the human eye respond most strongly to red, green and blue wavelengths, giving us our colour vision.
The first steps towards correctly explaining the colour of the sky were taken by John Tyndall in 1859. He discovered that when light passes through a clear fluid holding small particles in suspension, the shorter blue wavelengths are scattered more strongly than the red. This can be demonstrated by shining a beam of white light through a tank of water with a little milk or soap mixed in. From the side, the beam can be seen by the blue light it scatters; but the light seen directly from the end is reddened after it has passed through the tank. The scattered light can also be shown to be polarised using a filter of polarised light, just as the sky appears a deeper blue through polaroid sun glasses.
This is most correctly called the Tyndall effect, but it is more commonly known to physicists as Rayleigh scattering—after Lord Rayleigh, who studied it in more detail a few years later. He showed that the amount of light scattered is inversely proportional to the fourth power of wavelength for sufficiently small particles. It...