Re: Sunsets

[John Denker <jsd@MONMOUTH.COM>]

At 08:49 PM 8/29/00 -0700, Daniel Schroeder wrote:

> I disagree with your claim that my simplified model of
> scattering by an isolated molecule is irrelevant to the full explanation.

I didn't say it was 100% irrelevant.  I said "it is not the correct
explanation (and does not directly lead to the correct explanation) of the
red sunset / blue sky."

I also said it would lead to "an estimate of the index of refraction,
nothing more".

I stand by what I wrote.

> My model predicts the correct 1/lambda^4 dependence of the scattered
> intensity.

Do you have any evidence indicating that's actually the correct dependence?
If one unphysical calculation agrees with another unphysical calculation,
that doesn't prove that either one is correct.  Have you got any real data?

I could not immediately lay my hands on quantitative data for the spectrum
of blue sky-light, but I can tell you that photographers model it using a
color temperature of about 9000 K,
  http://www.fact42.com/light/articles/wave/wave.html
and if you look at the Planck spectrum, in the optical band the
alleged  lambda^4 dependence doesn't look anything like the 9000 K
spectrum;  it looks very much hotter than 9000 K.  To say it another way,
the blue of the sky isn't as deep blue as you might think;  it is not
nearly as deep as, say, the blue phosphor on your CRT.

>  The fact that there is then interference among waves
> scattered by different molecules, so long as the molecules are
> arranged randomly, does not change this dependence on the wavelength.

Actually interference does change the story, if there is a nontrivial
distribution of scatterers of different sizes, which there is.

I say again, the "molecule by molecule" calculation provides an estimate of
the average index of refraction, nothing more.  It is alas not the average
index but the _deviations_ from the average that produce the observed
scattering.

How are you going to explain to your students about optical fibers?  It is
well known that you can see through hundreds of kilometers of glass, with
negligible scattering.  The optical path in the glass contains orders of
magnitude more molecules than the optical path through the sky.  If the
"molecule by molecule" theory is correct, either the sky must be
transparent (i.e. stars visible in the daytime) or glass fibers must be opaque.

And by the way, how are you going to explain clouds?  A chunk of typical
fair-weather cumulus cloud has essentially the same number of air molecules
and the same number of water molecules as a chunk of clear air beneath the
cloud.  It has the same _average_ index of refraction.  One more time: it
is not the average index of refraction that does the job;  it is the
_deviations_ from the average.

Any "explanation" that stops with the molecule by molecule analysis,
ignoring the interference effects, fixating on the average index -- that
has about as much relationship to the real physics as a pot of water has to
a pot of soup.  It might be a starting point, but you shouldn't pass it off
as the finished product.