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So I know that when red and blue light (or the frequencies/wavelengths we percieve as such) hit our eyes with the correct proportions, our eyes and brains interpret that as the color purple.

In contrast, I have just read that that the bright emerald green color that severe thunderstorms can have is caused by tall thunderheads that are creating a lot of blue light through internal scattering that are then lit by red light from a late afternoon sun, and the combination of those two colors makes green.

Clearly what is not happening is that the red and blue wavelengths are not scattering separately in the cloud and then hitting our eyes, because then we should see the thunderstorm as purple.

So what is happening? How are the two colors being "mixed" or something in the cloud to create the wavelength(s) that we see as green?

Regarding the green clouds and whether the wavelengths are actually green or if it's an illusion, see: http://www.scientificamerican.com/article/fact-or-fiction-if-sky-is-green-run-for-cover-tornado-is-coming/

Related: Why does adding red light with blue light give purple light?

Frequency mixing seems to happen during scattering, so that is a clue to what's happening, but it's not clear to me if only some types of scattering cause frequency mixing or if all types do. If only some types cause mixing, then is one or more of those types caused by storm clouds? Assuming frequency mixing caused by scattering is the mechanism for producing green wavelengths, how are the other frequencies produced by mixing (e.g. overtones) not visible enough to affect the color perception (are they absorbed or not detected by human eyes or merely of too low intensity to matter)?

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Todd Wilcox
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This is a simple example of how red and blue light can mix so that they appear as green to the human eye. Let us take the example of two monochromatic time-harmonic light sources with frequencies $\omega_1$ and $\omega_2$. For simplicity let them both be cosines, then,

\begin{align} f(t) &= A_1 \cos(\omega_1 t) + A_2 \cos(\omega_2 t) \\ &= 2 A_1 A_2 \cos(((\omega_1 + \omega_2) t)/2) \cos(((\omega_1 - \omega_2) t/2) \end{align}

This is essentially an amplitude modulated cosine with a frequency varying in the THz regime, however our eye cannot discern the amplitude modulation so we perceive something like the time average. If $\omega_1$ is in the blue regime and $\omega_2$ is in the red region of the spectrum their wavelengths are something like,

$$ \omega_1 = 2 \pi \cdot 650 \, \text{THz}$$ $$ \omega_2 = 2 \pi \cdot 450 \, \text{THz}$$

and $(\omega_1 + \omega_2)/2 = 2 \pi \cdot 550 \, \text{THz}$, which is in the green region of the visible spectrum.

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CJRS
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