Re: The blueness of water

["John S. Denker" <jsd@MONMOUTH.COM>]

Robert Cohen wrote:
> ... it states "The lake's deep-blue color, for
> instance, results from the molecular backscatter of downwelling light,
> predominantly the short wavelengths in the visible light spectrum."
...
> 1. Is this statement correct?

As far as I can see, it is correct as far as it goes,
but it's so incomplete as to be somewhat misleading.

Pure water is reeeally clear.  A small or medium-sized lake
of pure water would be essentially totally transparent.

> 2. In a note by John Denker
> <http://mailgate.nau.edu/cgi-bin/wa?A2=ind0105&L=phys-l&P=R8112>, the graph
> <http://people.deas.harvard.edu/~jones/es151/pages/gallery/images/water_spec
> .html>2> is referenced which does not show any dependence of absorption on
> k^n in water.  Is there a k^n-dependence on scattering?

If you have a nonuniformity in the dielectric constant of a
medium, there will be a k^4 dependence in the scattering, even
if the dielectric constant itself is independent of k.  This is
a consequence of the basic scattering law.  An outline of the
derivation of the Born approximation can be found at
  http://www.monmouth.com/~jsd/physics/blue-sky.htm

> 3. Based on past discussions on this list, it seems that the wavelength
> dependence of scattering in air can be explained by assuming air molecules
> to be small dipoles but density fluctuations in the air are necessary to
> explain the k^4 dependence.  Is this correct?

I would say that the density fluctuations explain the
overall magnitude of the scattering.  The wavelength dependence
is the same independent of the overall magnitude.  See
the web page cited above.

It is a very, very common misconception to attribute the
wavelength dependence to the length-scale of the fluctuations,
but I'm pretty sure that's wrong physics.

> 4. My guess is that there would be no density fluctuations in liquid water.
> Is this correct?  What about a wavelength-dependence of scattering?
> Wouldn't the assumption of small dipoles still be correct?

My guess is that the lake is blue because of a "gas" of dissolved
and/or suspended minerals.  There will be density fluctuations in
this gas.  (There will be density fluctuations in the liquid, too,
but my intuition agrees with Robert's that these will be too small
to have any significance.)