I guess I've seen a handful of rainbows since I moved to Colorado in 2013. They're not a common occurrence here like they were in the much rainier South. The rain, the sun, and you have to be lined up in a certain way to get a rainbow.
My favorite rainbow memory is from my days as a welder's assistant on a pipeline barge in the Gulf of Mexico. We were installing a riser (the part of the pipeline that connects it to an oil well platform) and it was late on an overcast day. The sky was dark but the horizon was clear and where the sun was setting it was blood red, casting a deep red light across the underside of the clouds. Against that backdrop was a brilliant triple rainbow.
I had to get out our lawn sprinkler to get this one.
Here's how rainbows work. A rainbow is actually a cone. The part you see is where a sheet of rain intersects the cone - it's actually a circle. It looks like a bow because part of it is below the horizon or underground.
The apex of the cone, it's point, is at your anti-solar point. If you draw a line from the sun (don't try this) through your head (right between your eyes) and continue it down into the Earth, that's your solar axis. The anti-solar point is somewhere on the solar axis below you. Now, imagine a cone extending back toward you from that point.
The cone has an angle of 40 (the blue part) to 42 (the red part) degrees - that's the angle at which the light leaves the raindrops). That means that the sun has to have an angle of inclination of 42 degrees or less to see the rainbow. For my rainbow (the sun's angle of inclination is the same as the top of my shadow's angle of declination - only positive.
49.1° ... wait... that's more than 42°.
Hey, okay, notice that my rainbow was formed by a lawn sprinkler and it's below the horizon.
I mentioned that my favorite rainbow was a triple rainbow. If you ever see one of these, pay attention to the order of the colors. In a secondary rainbow, the order is reversed with the blue on top. That's because the light is reflected twice inside the drops. The drops that cause a secondary rainbow are completely different drops and the cone is at 51° to 54° of the anti-solar point.
Triple rainbow? Well, there are a lot of different kinds of rainbows. Some can be formed by light from the sun bouncing off the surface of a lake or the ocean and then hitting rain. If a rainbow is caused by sea mist, salt water has a different index of refraction than fresh water, so the angle of the cone will be different. Also look for rainbows in waterfalls and geysers. And if you're in a plane and see a rainbow in the clouds below you, you may be able to see the whole circle!
Rainbows are special, and rare. If you see one, see if it looks different than the one I described and see if you can figure out what makes it different.