# Mechanism for visible light frequency mixing in storm clouds

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/

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)?

• I have never heard of a green cloud. Googling only turned up a cloud of pollen over Russia. Do you have a reference? – mmesser314 Aug 3 '15 at 13:53
• Living in a place with thunderstorms on most summer afternoons (in a good year), I too can not recall a noticeably green thunderhead. Note, however, that blue and yellow will make green, and yellow is a common evening cloud color (yellow to orange to red as the sun sinks lower). – Jon Custer Aug 3 '15 at 14:00
• In the Washington, DC metro area, which is not famous for tornados or hail like the American midwest, we get at least one ominous green thunderstorm every summer. I've been about 100 feet from a tornado and I've run to my car to get shelter from golf-ball sized hail. Green skies in severe weather are very real, I assure you. Actually it's quite a beautiful effect. I hope one day you all get to see it from a place that is relatively safe. – Todd Wilcox Aug 3 '15 at 14:06
• Here you go: facebook.com/UpNorthLive/videos/992721894105840 – Todd Wilcox Aug 3 '15 at 14:26
• Looks like frequency mixing during scattering happens when scattering is caused by both free and harmonically bound electrons: nature.com/nature/journal/v225/n5239/abs/2251239a0.html Added optics and non-linear optics tags – Todd Wilcox Aug 3 '15 at 15:48

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.

• Okay, so the THz regime is just the frequency with which the electromagnetic energy corresponding to the light is traveling. It corresponds directly to the wavelength of the light by the formula omega = 2*pi*c/lambda where lambda is the wavelength of light. So frequencies in the THz regime are very "fast" since the wavelengths of visible light are very small. That is, fast in comparison to something like a phone or the internet which typically operate in the GHz or MHz regime. – CJRS Aug 3 '15 at 14:17
• There is at least one typo in your expression - should it not be $(\omega_1 + \omega_2)t/2$ for one of the $\cos$ terms? And doesn't frequency mixing require a nonlinear response of at least one element? Can you explain what element that is? – Floris Aug 3 '15 at 14:26
• @Floris Thank you, I've corrected it, the Latex interpreter on the browser I'm forced to use at work sucks so it's hard to catch some of the errors. – CJRS Aug 3 '15 at 14:30
• @CJRS - no worries, we all do it. That's why this is a "community"... – Floris Aug 3 '15 at 14:30
• You don't have to start and stop a math environment for every single variable. Check the edit history to see how I changed it. It's much simpler. – DanielSank Aug 3 '15 at 16:41