From: pauld@exploratorium.edu
Date: Mon Mar 27 2000 - 23:46:22 PST
Message-Id: <200003280746.XAA01180@isaac.exploratorium.edu> From: pauld@exploratorium.edu Subject: Re: pinhole Blue Skies Date: Tue, 28 Mar 2000 07:46:22 GMT
Hi Sidney
(I wrote my PhD thesis on the subject of light scattering from statistical
fluctuations of molecules per unit volume. So I am a world expert on this
topic.)
All you need to understand to explain the blue sky is thelight scattered by each
molecule. To understand why the sky is bright you need to understand light
scattering by statistical fluctuations in the number of molecules per unit
volume.
Essentialy if the air is a uniform dsitribution of molecules it scatters no
light at all.
However, being a gas in constant motion the number of molecues in one-half
wavelength cubed is different from the number in the next half-wavelength cubed.
This is well understood as a statistical fluctuation, if there are an average of
N molecules in a half-wavelength cubed then there will be a distribution of
molecule number characterized by a gaussian dsitribution with a width of the
square root of N. The blue molecule wavelength encapsulates a smaller number of
molecules than the red wavelength so the fractional difference in number from
one wavelength to the next is greater for the blue. However the strength of te
scattering depends not only on the fractional number, it also depends on the
total number of scatterers. There are more scatterers in a cubic half-wavelength
of red light than blue. The effects cancel and the result is a blue sky
scattering that depends on the scattering by individual molecules.
So the other author considered only the first half of the answer.
The effect doesn't cancel when the light hits a water drop, in one half
wavelength there is air, in the next water. So the amount of scattering here
depends purely on the number difference from one region to the next. There are
far more molecules in a cubic half-red wavelength of water than in a blue half-
wavelength. A number proportional to the cube of the wavelength. This effect
then scatters more red light proportinal to te cube of the wavelength while the
resonance effect due to the molecules is proportional to the inverse fourth
power. The effect of the nmber here cancels the effect of the scattering
(almost) This is why clouds are white..
Paul It's more complcated than that D
> Paul's explanation for why the sky is blue sounds right, but I remember
> reading another explanation by an author who seemed very confident (it might
> have been James Trefil). He said it was really a matter of statistics.
> Light is scattered in the sky predominantly by groups of molecules, not
> single atoms or molecules. A small number of molecules in the right
> configuration scatters blue light, since the group's small size makes it
> scatter a shorter wavelength, while a larger group scatters red light whose
> wavelength is longer. Statistically the smaller group of molecules is more
> common than the larger group, since it contains less molecules which have to
> fall by chance into the right places, so the sky scatters more blue light
> than red.
> Has anyone heard of this alternate explanation, and does it have any merit?
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