How Rainbows Form: The Journey of Light Inside a Raindrop
✦ Key takeaways
- A rainbow is an optical phenomenon produced by refraction, dispersion and internal reflection inside raindrops, not a physical object with a fixed location.
- The primary bow forms from a single internal reflection and appears at about 42 degrees opposite the Sun, with red on the outside and violet on the inside.
- The fainter secondary bow comes from two internal reflections, appears at about 51 degrees, and has its colors reversed.
- The color order is fixed because each wavelength refracts at a specific angle; violet bends more than red.
- You can never reach the end of a rainbow because its position depends on your viewing angle and moves with you.
Picture yourself standing after a summer shower, the Sun warming your back, when a band of color arches across the sky so close you could almost touch it. That arc is not an object suspended in space; it is an image painted by sunlight as it passes through millions of water droplets at once.
The Raindrop as a Tiny Prism
Every raindrop acts as a lens, a mirror and a prism all at once. When a beam of white sunlight enters a drop, it bends at the surface because light travels more slowly in water than in air. It then bounces off the back inner wall in an internal reflection and bends again as it leaves. Together these steps redirect the beam and split white light into its colors.
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White light is really a mixture of different wavelengths, and each wavelength refracts at its own angle. This spreading is called dispersion, and it is what separates white into a continuous spectrum from red to violet.
Step by Step Inside a Drop
Let us trace a ray in the primary bow. First, the ray enters the front surface of the drop, refracts and begins to separate into colors. Second, it crosses the drop and strikes the back wall, undergoing a single internal reflection. Third, it returns to the front surface and refracts once more as it exits into the air. The net result is that light leaves at a total angle of about 42 degrees for red and about 40 degrees for violet.
This is why the bow is seen only in one direction: only the drops that send their light to us at precisely this angle form the colored band, while the light from all the others passes harmlessly past our eyes.
Why 42 Degrees, and Opposite the Sun?
The rainbow is centered on what is called the antisolar point, the imaginary spot directly opposite the Sun, along the line from the Sun through your head to your shadow. The primary bow traces a circle with an angular radius of roughly 42 degrees around that point. Because the Sun sits above the horizon, we see only part of the circle as an arc. The lower the Sun, the higher and fuller the bow; once the Sun climbs above 42 degrees, the bow drops below the horizon.
The Double Rainbow and Reversed Colors
Sometimes a second, fainter bow appears outside the first. This secondary bow forms when light reflects twice inside the drop instead of once. The extra reflection reverses the color order and scatters more of the light, so it looks dimmer and appears at a larger angle of about 51 degrees. The relatively dark region between the two bows is known as Alexander's band.
| Property | Primary Bow | Secondary Bow |
|---|---|---|
| Angle from antisolar point | about 42° | about 51° |
| Internal reflections | 1 | 2 |
| Color on outer edge | red | violet |
| Color on inner edge | violet | red |
| Brightness | bright | faint |
Why the Color Order Never Changes
The order of the colors is fixed because it is set by physics, not by chance. Shorter wavelengths such as violet bend at a greater angle than longer ones such as red. In the primary bow, red exits at a wider angle and lands on the outer edge, while violet lands on the inner edge.
| Color | Approximate wavelength | Position in primary bow |
|---|---|---|
| Red | about 700 nm | outer edge |
| Yellow | about 580 nm | middle |
| Green | about 530 nm | middle |
| Blue | about 470 nm | toward inner |
| Violet | about 400 nm | inner edge |
Why You Can Never Reach the End
Because a rainbow is not a place but an angle. Its position is defined relative to your eyes and the Sun, so as you move it moves with you, always holding that 42-degree angle. Each person really sees their own rainbow made from different drops, and even your two eyes see slightly different bows. That is why the end of the rainbow stays forever out of reach: run toward it and it slides away like a colored mirage.