Re: Sunsets

[John Denker <jsd@MONMOUTH.COM>]

At 11:53 AM 8/30/00 -0700, Daniel Schroeder wrote:
> In a solid or liquid, the spacing between adjacent molecules is pretty
> uniform, so the interference of scattered light from different
> molecules will be much more complete than in a gas, where the molecules
> are more or less randomly distributed.

That's a step in the right direction.  Keep going in that direction and
you'll get to the correct physics.

Try to quantify what it means to say "pretty uniform" versus "more or less
randomly distributed".

Consider a region in the atmosphere so small that coherence is
guaranteed.  A cell lambda/2pi on a side should be small enough.  Ask
yourself how many thousands of air molecules there are in such a cell --
all scattering coherently, guaranteed by construction.

Argue from the most elementary statistical principles that any two such
cells have "pretty much" the same number of molecules, and that therefore
the troposphere is more like glass than like a collection of independent
Rayleigh scatterers.

======

A lot of students find the correct analysis counterintuitive because they
don't have a good intuition about the relevant magnitudes:  the size of
atoms, the spacing between atoms, and the wavelength of light.

Mnemonic #1:  atoms are small, a thousand times smaller than light.

Mnemonic #2:  common substances (water, nitrogen, ...) expand in volume by
a factor of roughly 1000 when going from liquid to vapor at STP or
thereabouts.
Corollary: In the gas the intermolecular spacing is about 10x the molecular
size -- still tiny compared to light.