Originally posted by Tom
Which mathematical phenomenon? There is nothing mathematical in rainbow (contrary to your faith).
Oh, my god. Nothing mathematical, huh?
Tom, did you study optics? Dispersion of light? Atomic physics? There is PLENTY of mathematics in explaining why the electrons in glass respond to e/m field of different frequency differently.
Rainbow, contrary to your claim, is not a physical phenomenon. There is no rainbow per se (=by itself). It is the mathematical result of interaction of several more basic objects/phenomena.
Now, let's honestly ask ourselves: does rainbow bow originate from light itself? Nope. There is no rainbow in sunlight. Indeed, look at the Sun - do you see the rainbow? Nor there is a rainbow in a droplet of H
20. Again one can take a droplet and attempt to get rainbow out of it (without adding sunlight or other light). But adding them together (droplet AND sunlight) and looking at their interaction at certain angle - voila - we observe a rainbow circle. And the dispersion of electron's respond to e/m wave is key factor in creating rainbow out of light and water. The shape of rainbow, the location and the order of colors are dictated by dispersion function of respond of outer electron in O atom in a water molecule to passing e/m wave.
So, we need several ingridients to cook a rainbow: mix of photons (sunlight), spherical droplets, and dispersion of electron interaction. Then a rainbow with all its "physical" properties follows as a mathematical consequence.
Each of "appear to be physical" ingridients (say, sunlight, or electron) can be analysed futher (as another object) and similarly found to be a mathematical consequence of more fundamental "parts". And so on.
So, there is not as much "physics" in a rainbow as you think. But much more math resulting in all its observable properies: angular radius of rainbow, location, colors order, colors angular separation, overlapping of wavelengths (due to angular size of Sun), spread of individual colors (due to diffraction on droplet), angular size of second reflection created rainbow, inverse order of colors in that rainbow, etc etc - all these properties are mathematical consequence of interaction of light with distribution of droplets PLUS the location of observer (system of reference). What can be seen by one observer (in one system of reference) can not be seen by another one (say, in shifted reference system) despite that both observer look at the SAME water droplets illuminated by SAME light.
It is plenty of math, dude.