The Physics of the Rainbow
A rainbow is sunlight, rain, and geometry combined. Explore the physics of the rainbow and why it always appears as an arc.
A rainbow is one of the most beautiful sights in nature, and one of the most reliably mysterious. It appears after rain, arcs across the sky, and vanishes when approached. Behind its beauty is a precise and satisfying piece of physics—an interaction between sunlight and raindrops.
Sunlight Is a Mixture of Colors
The first ingredient is sunlight. Although sunlight appears white, it is actually a mixture of all the colors, each corresponding to a different wavelength of light.
Normally these colors travel together, blended into white. A rainbow is what happens when raindrops separate them out.
What Happens Inside a Raindrop
The heart of the rainbow is what happens when a ray of sunlight enters a single, roughly spherical raindrop. Three things occur in sequence:
- Refraction on entry: as light passes from air into the denser water, it bends. Crucially, different colors bend by slightly different amounts—so the colors begin to spread apart.
- Reflection inside: the light travels through the drop and reflects off the back of the drop's interior surface.
- Refraction on exit: as the light leaves the drop and re-enters the air, it bends again, and the colors spread apart further still.
The net result: a ray of white sunlight enters the drop, and a fan of separated colors emerges, sent back at an angle.
Why a Rainbow Is an Arc
This explains the colors, but why the distinctive arc?
The geometry of refraction-reflection-refraction means that each color leaves the raindrop concentrated at a particular, specific angle relative to the incoming sunlight. Red light emerges at a slightly different angle than violet, and so on.
For you to see a particular color, light of that color must reach your eye from a raindrop sitting at exactly the right angle. The set of all points in the sky at that precise angle, relative to the line from the sun through your head, forms a circle—or, with the ground in the way, an arc.
Each color forms its own arc at its own slightly different angle, and the arcs nest together into the familiar band. The rainbow is, in essence, a map of angles.
Why a Rainbow Belongs to You
A subtle and beautiful consequence follows. Because the rainbow's position depends on the angle between the sun, the raindrops, and your eye, the rainbow's location is specific to your viewpoint.
Another person standing nearby sees a rainbow formed by different raindrops, at the same angle relative to their eye. In a real sense, every observer sees their own rainbow. And this is also why you can never reach a rainbow—as you move, the geometry moves with you, and the rainbow keeps its distance.
Light, Water, and Geometry
The rainbow is a perfect example of how physics underlies beauty. It is nothing more—and nothing less—than sunlight, raindrops, and the precise geometry of how light bends and reflects. Understanding it does not diminish the wonder; it deepens it. The next time an arc of color appears after the rain, you can see it for what it truly is: a piece of pure science, painted across the sky and addressed, uniquely, to you.