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My current understanding is: this can be described mainly as Rayleigh scattering: Incoming white light from the sun is scattered by particles with resonances in certain wavelengths. The wavelengths that are most resonant wiggle the outer electrons the most, and that wiggling produces light in the same wavelength as the light that initially wiggled it. I also understand that a particle's ability to scatter light of a given wavelength is at least in part a function of its size, but the details of how particle size relates to the frequency scattered confuse me. I know glacial lakes often appear green in the spring and blue in late summer and my current understanding is that larger silt particles scatter green light and smaller clay particles scatter blue light. In the spring the silt particles are washed into the lake in the melt out and then the larger particles settle out over the summer.

What I don't understand is:

If the frequency of light scattered is a function of particle size then why do particles of vastly different sizes (milk fat particles, clay particles, and atmospheric particles) scatter many of the same wavelengths (look blue to humans)? If I wanted to craft some particles to stir into water to make it look a given color what am I looking for in the particles?

I'd love to get a look at a diagram that gives a model for what happens at a molecular level when light hits a particle that scatters primarily blue/uv vs a particle that scatters primarily green.

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  • $\begingroup$ Remember that $\text{H}_2\text{O}$ is already blue by itself and doesn't need any suspended particles to appear blue. It just only appears colorless in small amounts. $\endgroup$
    – Triatticus
    Commented Aug 24, 2022 at 21:07

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This is actually a little complicated. Glacier lake water is very very nice water compared to ocean water. In ocean water you have a lot more dissolved ions, salts, inorganic particulate, dissolved organic matter and resulting acids as well as plankton etc. Compared to distilled water glacier water probably will has a bunch of stuff in it, but at first pass in the ultraviolet you have the harmonics of electronic transitions increasing the absorption and in the infrared you have absorption of from molecular O-H bonds. So even in water without salts you have a transmission window in the blue and green.

For the very pure water without particulates the best transmission is around 405 nm in ocean water near the coast to the various scattering and absorption the best transmission may be around 520 nm or even longer. As you go from the coast to deep ocean you will be very surprised by the color change. For example taking a ship to Hawaii you will be surprised how green the water is compared to being out far from land. Of course if you fly in you will think the Hawaiian water is very very blue and clear. So there is some perception of color involved.

But to answer your question for Rayleigh scattering to matter the size of the interaction should be less than about 1/10 the wavelength of light. If the particles are larger the Mie scattering dominates, And with Mie scattering you have a much more forward scattering and back scattering as compared to Rayleigh scattering. If the particles are very large compared to the wavelength then the scattering is geometric.

The wavelength dependence of Rayleigh scattering is much more wavelength dependent than Mie scattering. So in air as molecules get polarized by the oscillating electric field they more efficiently scatter the blue. Smokers sometime notice that cigarette smoke has a blue tinge, but when they exhale the smoke is whitish in color. The tiny carbon particles when exhaled are surrounded by water and are larger so the scattering mechanism is different.

Another aspect is if you have multiple scattering or only one or two scattering before the photon is absorbed. Milk for example with lots of fat globules pretty large is probably Mie scattering with multiple scattering going on so like clouds looks white.

The ratio of scattering length and absorption kind of like ‘albedo’ is one way to compare different waters with different amount scattering particles and amounts of absorption.

With the silts you mention you have different suspensions, but you also probably have some different geometry of the particles. That matters some if you do the electromagnetic calculations but not as much as you might think in terms of wavelength dependence. You also probably start out in the spring with a lot more variation of the size of particles, and perhaps also more organic acids that also absorb the blue more.

Then later in the year you probably have a much smaller distribution of particle sizes as well as the particles being more uniform in shape. The smaller particle size with less forward scattering as well as less multiple scattering. I would guess that you also have less dissolved organic material so less of that absorption in the blue, but I don’t know how much that contributes.

Hyperphysics has a good cartoon model of the difference of how Rayleigh scattering and Mie scattering, as a function of direction. If you do the Mie scattering calculations it gets complicated with minimums and maxima in the scattering function.

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