Colour  by  Scattering

13th April 2001

The sky is blue, except, as the second and third pictures show, when it isn’t.  Air is not in itself coloured, and even if it were, it is transparent, so you might expect it to look black, because only empty space is behind it.  But in fact it affects light in an unexpected way.  The reason is that different wavelengths are affected differently by obstacles.  The many legs of a seaside pier have little effect on very long waves, but little ripples are scattered around by them.  Where are the obstacles in air?  Air is made of tiny molecules, in such huge numbers that when you breathe in you are likely to have taken in a few molecules breathed out in a single breath by any one historic person you care to name, as long as the air has had time to diffuse around the world, and has not been absorbed.

These molecules are not the actual obstacles, but because they are moving around, they are not uniformly distributed, on a microscopic scale.  It is the variations that constitute the scattering centres.  This type of  scattering, called Rayleigh scattering, is very strongly dependent on wavelength.  In fact, halving the wavelength multiplies the amount of light scattered by a factor of sixteen.  Violet and blue light is scattered much more than red and yellow, because those colours have shorter wavelengths.  So the sun appears to be a little more yellow than it really is, because some of the blue is taken out of the direct path to make the blue sky.  What happens is that some sunlight that would have reached you is deflected away towards someone else.  And you in turn get some of "their" light.

The colour bias caused by Rayleigh scattering can only be towards the short wavelength end of the spectrum which is visible to any animal.  So it can never cause a red sky for humans.  The sky of Mars is coloured by the dust from the reddish rocks.  The diagram below shows the spectrum of radiation of the sun versus frequency (grey), and the result of multiplying the same curve by the Rayleigh scattering formula (blue).  The blue bias in the scattered light is evident.  The two curves have been normalised to the same height, but of course the Rayleigh curve can never be higher than the solar one.

Adding direct sun light to sky light gives daylight.  A photograph taken in the shade may look blue unless it is corrected, because it is illuminated only by the blue sky.  This is why some Impressionist painters put blue shadows in their pictures.  If you read a book in the shade, you don’t normally see the paper as bluish, because vision is a complex process which can make allowances for variations in lighting.  Photographic slides taken of objects in the shade can show a bluish cast.  Prints may not show the cast because the printing may compensate for it.

At high altitudes there is less air above, and so the sky looks darker, giving a clue that without Rayleigh scattering, lighting on earth would be as harsh as it is on the moon.  Some idea of the effect is obtained in a a street with one lamp, or in a black-painted room lit by a single bulb.

The light from the sky is partially polarized. (Polarizing)  This effect is used by bees to orientate themselves.

Question – Is fresh cigarette smoke blue because of Rayleigh scattering?  If so, when illuminated from the side, its appearance should be affected by a polarizing filter.  Why does the smoke go grey with age?

If the air makes the sun look less blue, then at sunset, when you are looking through more air, the sun should look even less blue than usual.  It does.  And the colour of sunsets can be enhanced by dust in the air.  How much air are we looking through when the sun is on the horizon?  Let’s take the height of Mt Everest as the average height of the atmosphere, as a rough guide.  This is about 9000 m.  The radius of the earth is about 6400 km.  From these two figures we get 340 km.  This means that we are looking through about 38 times as much air as when the sun is overhead. No wonder that the sun doesn’t look the same.  This calculation underestimates the effect of the air because the part of the path nearest the observer is almost parallel with the ground for many miles, contributing air at its maximum density.

Some people find blue eyes very attractive, as evidenced by "Old blue eyes", "Don’t it make my brown eyes blue", "A pair of blue eyes", "Blue eyed boy."  The first three are associated with Frank Sinatra, Crystal Gayle, and Thomas Hardy, respectively.

Pure blue eyes have no pigment in the irises.  The blue is caused by Rayleigh scattering.  It may fade to grey as time passes, because the scattering particles in the iris expand.  If small amounts of pigment are present, the iris may take on colours ranging from blue to green.

The blue of some lizards is also caused by Rayleigh scattering.