Monday, June 1

Rainbow

Of course, if one wants to be really pedantic, I guess we could say it is a constantly changing rainbow for each of us since the light of any given wavelength arriving at our location in those beautiful arcs is always coming from different droplets as they fall. Or, if you blink, you are now seeing a different rainbow.

On the other hand, the light source is the same - the Sun, the field of droplets is the same (without thinking about individual droplets), and all the angles are the same.

The geometry of reflection, however, is such that all the droplets that reflect the rainbow’s light toward you lie in a cone with your eyes at the tip.

Water droplets reflect sunlight (or any light) at an angle of between 40 and 42 degrees, depending on the wavelength.

Because of the sharp angle, you only see rainbows when the sun is (1) behind you and (2) low in the sky. When the sun is high, the light reflecting off the droplets passes over your head and you see nothing.

Now for a little creative visualization. The sun is low and behind you. All the sunbeams head in, strike the cloud of water droplets ahead of you and bounce back at an angle of 40 degrees.

Naturally the beams can bounce 40 degrees any which way — up, down, and sideways. But the only ones you see are the one that lie on a cone with a side-to-axis angle of 40 degrees and your eyes at the tip.

Don’t get it? OK, face a wall and extend your arm so it’s at 40 degree angle thereto. Now rotate the arm in a full circle, keeping the 40 degree angle to the wall. Your arm describes a cone, right?

If you think about it, you should be able to convince yourself that the only parts of the wall that are at exactly a 40 degree angle to your shoulder lie on that cone. Same with rainbows.

I said that water droplets reflect light at an angle of 40-42 degrees. Usually they do. But sometimes the light bounces around twice inside each water droplet and exits at an angle of around 51 degrees. So you’ll see a second rainbow above the main one with the colors reversed. It is fainter, but be kind. It is doing the best it can.

Articles:
Why are rainbows curved? Rainbow Formation

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