We’ve been told (and some choose to believe) that rainbows are only illusions, and rainbows have nothing to hide. Kermit says no, and so does the math of optics. Using the path of sunlight through single drop fo water, mathematicians can describe how rainbows work. Here’s more from Rashida over at her math blog, iRashida:
This seems like a very cool phenomenon, because it means that the rainbow’s location is independent of both the size and location of the water droplets that form it. It is also pretty cool because this number, , can be derived from looking at the behavior of light inside a single droplet of water. Rainbows are typically formed out of thousands of drops of water, but we can understand something about them by examining just one.
So lets look at the path of sunlight through a raindrop, represented by the solid yellow line in this diagram.
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