Rain into color: The physics of rainbows

At the end of a rainy day, you might check the sky to catch what is one of our world’s greatest marvels. An arc of colors stretches across the sky amid the receding gloom of the day, and creates a bright and beautiful rainbow.  Although the joy caused by rainbows is often shared, no two people see the same rainbow. The colors you see are from a unique alignment of the sunlight, raindrops, and your eyes.

Rainbows form because of the specific path light takes when it interacts with water droplets. The first interaction between the water and the light is called refraction, which simply describes the bending of light. When light passes from air into water, it experiences a slight delay which ultimately slows the light down. 

This phenomena can be observed as light bending in another direction. But, the degree to which the light bends is different for each color of light. Red light bends the least and violet light bends the most. As a result, when sunlight enters the rain drop, it begins to separate into a range of colors, much like what happens when light shines through a glass prism.

The next interaction in the process is reflection. The refracted light travels to the back of the raindrop where it reflects, similar to light bouncing off of a curved mirror. Finally, the light heads back to the front of the droplet and exits. The individual rays of colored light refract once again and separate even more, just enough to make them distinct enough to differentiate. The refraction process bends the light into its own special angle dependent on color. For red, this is about 42° and for violet, 40°. The other colors fall in between. 

At the instant you look at a rainbow, you are observing the refracted light from billions of different, yet perfectly suspended droplets all at once. Every single refracted ray that meets your eye at 42° will build up the red band. The following colors of the rainbow come from an entirely different set of raindrops that are momentarily at just the right angle. Because the angle between your eye and the raindrops must be so exact, no one else can see the same rainbow as you.

Now, consider some of the special details you can see in rainbows. Have you ever noticed that the sky appears brighter below rainbows than above them? This has to do with those special angles. While droplets won't send much light to your eyes at angles larger than 42°, angles below that will send a lot of light. 

As the colors blend in the lower region of the sky, you receive lots of white light and the region appears brighter. On the other hand, droplets at angles above 42° don’t send as much light, creating a dark region in the sky called Alexander’s Dark Band.

Sometimes when you look at the sky, you see a double rainbow. Double rainbows form when light reflects twice inside of the raindrop. That extra reflection changes two things about the resulting rainbow: the direction the light leaves and how bright the light is. The second reflection causes the light to exit at around 50°, so the secondary arc sits just 8° above the primary one. Each time a ray internally reflects, it also refracts into the air outside of the droplet, dividing the amount of light that’s actually visible in the rainbow.

Something as simple as a glance at a rainbow is the result of countless tiny optical events happening all at once. You can thank physics for creating a colorful spectacle that is uniquely yours.