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Bohren on blue sky and sunsets



Now that I've read Bohren's article in The Physics Teacher
(May, 1985, page 267), I can recommend it with unreserved
enthusiasm. Please, don't take my word for it, go read it
for yourself. However, for the impatient, here's a summary
of some of the points made:

First, Bohren (with coauthor Fraser) paraphrases Rayleigh's
dimensional analysis "derivation" of the inverse-fourth
power law for scattering by objects smaller than the wavelength.
This is a nice argument which I had never seen before.

After a discussion of why the sky appears blue rather than
violet, the authors then explain that adding more scatterers
to the atmosphere (e.g., small particles in addition to molecules)
will increase the brightness of the sky but not the blueness.
The reason is multiple scattering: While the added scatterers
increase the amount of long-wavelength light scattered toward
your eyes, they don't increase the amount of short-wavelength
light as much because this light is likely to scatter more
than once, and the additional scatters don't help. This is
why the sky on the horizon generally appears white rather than
blue. (This effect is particularly striking from airplanes.)

On the other hand, adding more scatterers to the atmosphere
*does* make sunsets redder (and dimmer). The authors calculate
that in a pure atmosphere at sea level, the sun on the horizon
should appear orange. Only a couple of degrees above horizontal,
it should appear much more yellowish. To get a deep-red sunset,
you need additional scattering by small particles in the
atmosphere.

And what about the issue of density fluctuations in the atmosphere?
Irrelevant for an ideal gas, according to Bohren and Fraser.
They claim that, since the molecular positions in an ideal gas
are uncorrelated, the total scattering rate is just N (the number
of molecules) times the molecular scattering rate. Jackson
(second edition, page 422) agrees. Density fluctuations are
important (they say) in liquids and high-density gases. I'm not
sure I fully understand this issue myself, though.

Happy sunsets,

Dan