I first learned about the physics of rainbows in 8.03, sophomore physics, which I took from Walter Lewin. I have never looked at rainbows the same way since. You can watch Prof Lewin’s complete 8.03 lectures on YouTube here.
Rainbows are based on dispersion, that the speed of light in water depends on its frequency or wavelength. Dispersion and internal reflection contribute to the very specific set of conditions to see a rainbow. The ray diagram for difference colors through a water droplet is shown in the figure here.
This means, to see a rainbow, you need three important conditions:
- The sun has to be behind you.
- Water droplets have to be in the sky in front of you
- The sky must be clear between you and the water droplets, and there is a direct view of the sun to the water droplets
To see the rainbow, stand with the sun at your back. Draw an imaginary line from the sun through your head. Extend your hand along this line and raise it up 42 degrees. Trace out the cone from horizon to horizon at this 42 degree arc. If the conditions are good to generate a rainbow, you will see it.
A primary rainbow is due to one internal reflection of light inside the water droplet. The red light will always be on the top of the primary rainbow arc.
When there are two internal reflections of the light, the secondary rainbow will be above the primary and the colors reversed, as shown in this figure. There will always be a secondary rainbow. Its only when you have a dark background that you can see this secondary rainbow.
Between the two arcs of the primary and secondary rainbow, there is not refracted light. This means the region of the sky will not have refracted light coming from it, and it will be dark. These effects are exactly what I see in the picture I took of the double rainbow from Longmont, CO on Aug 1, 2019 in the picture at the top of this column.
Just because I think about dispersion and total internal reflection when I see a rainbow doesn’t mean I don’t think they are beautiful. It means I also think they are a pretty cool demonstration of how we can take the fundamental principles of physics and apply them to the real world. Physics works.
