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Re: The blueness of water



Water is a weak selective absorber - it absorbs more strongly in the red
region than in the blue. It is a blue liquid.

The optical properties of water are described in a number of places:

See:
"Why is Water Blue?," C. L. Braun and S. N. Smirnov, Journal of Chemical
Education, Volume 70, Number 8. August 1993, pp. 612-614.

The n and k values of water are tabulated in:
Handbook of Optical Constants by Palik.
In the visible region:

Wavelength n k
(nm)
300.0 1.371 4.148e-9
325.0 1.364 3.082e-9
350.0 1.358 2.528e-9
375.0 1.354 2.031e-9
400.0 1.35 1.58e-9
425.0 1.347 1.169e-9
450.0 1.344 8.087e-10
475.0 1.342 7.011e-10
500.0 1.339 9.243e-10
525.0 1.338 1.64e-9
549.0 1.336 2.442e-9
575.0 1.334 3.844e-9
600.0 1.333 9.634e-9
625.0 1.332 1.472e-8
650.0 1.331 1.674e-8
674.0 1.33 2.177e-8
700.0 1.329 3.348e-8
725.0 1.328 9.137e-8
750.0 1.327 1.559e-7
775.0 1.327 1.478e-7
800.0 1.326 1.25e-7

and at:
http://www.icess.ucsb.edu/hydro/aviris/optics.html

And an excellent discussion of this topic is given by Craig Bohren in Clouds
in a Glass of Beer, pages 155-160.

A higher density of particulates in water will lead to light being reflected
out of the water, having traveled a shorter path length in the water. That
shorter path length will lead to a less distinct color. (Note that for
really short paths - like a glass of water), the selective absorption is not
noticeable and water appears colorless.)

If there are few particulates in water, the light path will be longer before
the incident light is scattered out, leading to a bluer color.

This is analogous to why the color of ice is an indication of density of
scattering centers (impurities or bubbles) in the ice.
See: http://www.sci-ed-ga.org/modules/materialscience/colorofice.pdf


Larry Woolf; General Atomics; 3550 General Atomics Court, San Diego, CA
92121; Phone:858-526-8575; FAX:858-526-8568; http://www.sci-ed-ga.org

-----Original Message-----
From: John S. Denker
Sent: Thursday, April 25, 2002 1:07 PM
Subject: Re: The blueness of water


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.)