Rainbow from the dark

First lets start off by pointing out something peculiar about rainbows. They occur in prisms, and on a rainy day under the right conditions, and in the spray of sprinkler, and they appear to move like fixtures suspended in the air moving with your perspective. Very strange indeed....

So this is a clue that we need to work with simple principles. Let's start with the familiar prismatic rainbow. What's on the inside? Inside a prism there are polished reflective surfaces. But there's a problem with the concept of reflection. If reflections were truly reflections it would mean the light being reflected actually stops and turns around as though it is being obstructed by a rigid body. Rigidity would mean instantaneous changes across a body and this is not possible due to causality. So we need to describe reflections instead as moving summations or interference patterns, which can change their direction by moving the relative center of the interfering constituents which are of course spherical wave fronts.

So why are the waves spherical? Well that my friend is caused by the uniformity of a point. Since a point is an infinitesimal in all directions then the expansion must be completely smooth with no deviations. In essence a spherical expansion. Now we must determine the cause of rate, or frequency. The answer is of course geometric. So what's something simple that radial or spherical waves inscribe? Deprecated: (Aha that's it: they inscribe concentric rings or concentric spheres. So What happens to those spheres as you approach the center of the source of emission? They get smaller of course. With this decrease in size you would see a decrease in the time it takes for the front to be passed over. A shortening of the rate or wavelength.) Edit: Spiral trajectories from the presence of mass which allows for angular momentum.

What about the glass? Like the glass in a prism? How is it see through? That can be answered simply using interference. The glass contains no or very little electromagnetic radiation in the visible spectrum so visible light does not interfere with it. It simply passes through it without any change in the pattern.

Okay now about those surfaces.... the polished surfaces are reflective but in the sense that we've already spoken about. So how is the prism doing the work of breaking up the spectrum? Well you have multiple reflective surfaces. What happens when you show a mirror itself? That's right! It's dark. Just like the song... ahh you see what I did there? Nah? Ahh you know what I mean hahaha.... ahhh... no? Never mind. Moving on.

So now all that's left is the angle. The angle increases the length thereby increasing the distance to the center of the source of emission which means you'll see a spectral dispersion of the light at different angles. The red is at the largest angle and the violet is at the shortest, and the concentric rings formed by the spherical wave fronts will be at the largest and shortest at those respective parts and the rest is in between on a continuum.

So there you have it! Rainbow from the dark!

But wait there's more! As bonus now you can also determine why the sky is blue during the day, and red near the dawn and in the clouds, and transparent at night! Now the traditional answer is that nitrogen has electron orbitals which are excited to a higher orbital by the light from the sun and then descend and release light in the blue portion of the spectrum. Which is still true in a way, but there's a little more to the story, and the way scientist talk about atomic structure and interactions probably has more to do with the utility of a mental model that works well when it comes to making predictions about how the matter and light behave. In order for the sky to radiate blue light we need two things: 1. the interference pattern that we call nitrogen must contain a large amount of blue light, and the light from the sun must be in that portion of the spectrum as well. Both those things are clearly true as you can see, and the atmosphere is closer to the sun than the clouds so that's why as the sun descends the distance to the clouds causes that red hue while the sky still remains blue. Then at night there's no or very little light from the sun to interfere with the constituents of the atmosphere so it's transparent!

Once again thanks for reading. Hope you enjoyed my article.