1. How a Single Raindrop Sorts Sunlight into Colors
Start with what happens to one ray of sunlight. It enters a raindrop and bends, which is called refraction. Some of it bounces off the curved inside back wall of the drop, like a tiny mirror, and then bends again as it leaves, heading back toward you[1].
Sunlight is a mix of colors, and each color bends by a slightly different amount. So the colors fan out as they pass through the drop[1]. Here is the surprise. For a particular observer and viewing angle, each drop mainly contributes one part of the spectrum to the bow. A drop higher in the sky sends you red, a drop a little lower sends you orange, and so on. Millions of drops, each adding its own part from its own position, add up to the band you see. A rainbow is not painted on the rain. It is sunlight being sorted by the rain, and where you stand decides which drops you see doing the sorting. That is the key to our question.
2. Descartes Measured Why the Main Rainbow Appears Near 42°
In 1637, the French thinker René Descartes published a set of essays that included one on weather, Meteorology. To find out where in the sky a rainbow's colors should appear, he did something that sounds almost too simple: he let sunlight shine through a large glass flask filled with water, which works like one giant raindrop, and he measured the angles of the light coming out[2][3].
What he found is that the bright red light reaches the eye at an angle of about 42 degrees in his setup[2]. That is the same 42 degrees the U.S. National Weather Service gives today for the main rainbow[1]. It also explains why a rainbow is a curved band: the drops that send you red are all the ones sitting at that same angle, which traces out part of a circle around the point directly opposite the Sun. Where that circle sits depends on where your eyes are, which matters for our question.
Descartes also worked out that the main rainbow involves two refractions and one reflection inside each drop[2]. But when he tried to explain why the colors appear at all, he imagined tiny spinning particles of light, with faster spinning making red and slower spinning making blue[2]. That explanation did not hold up. The real answer came a few decades later from a man with a prism.
3. Newton Showed That White Light Already Contains the Colors
Descartes could place the colors in the sky but could not explain why they exist. In 1666, when Cambridge University in England closed because of the plague, Isaac Newton was back at his family home in Lincolnshire, experimenting with sunlight and prisms, the triangular glass blocks that turn a beam of white light into a rainbow-colored strip[4]. One question was whether the prism was tinting the light or only revealing colors already in it.
So he set up a test. He let one color from the first prism, red for example, pass through a second prism. If the prism were painting the light, the red might change. It stayed red[4]. The colors were already there, hidden inside the white light, and the prism simply bent each one by a different amount. Newton described this in his first paper for the Royal Society, published in early 1672[4].
A nineteenth-century biography describing Newton's work adds a neat reverse trick: the spread-out colors can be brought back together into white, either by a second prism turned the other way or by a lens that gathers them into one spot[5]. Take light apart, put it back together, and it is white again. Raindrops do the same kind of sorting to sunlight, only with no glass in sight.
4. Why the Fainter Second Rainbow Has Its Colors Reversed
A second rainbow is a good test of the drop-by-drop picture. Sometimes a fainter one appears above the main one. If you look closely, its colors are in reverse order: red is on the outside of the main bow, but on the inside of the second one[1][3].
The cause is one more bounce. Light in the main bow reflects once inside a drop. Light in the second bow reflects twice, and leaves the drop at about 50 degrees instead of 42[1]. Descartes had already noticed the two-reflection path[2]. The extra reflection flips the order of colors[3], and since some light escapes at each bounce, the second bow is fainter.
Between the two bows, the sky often looks darker than the sky around it. That patch is called Alexander's band[3].
5. Why Two People Cannot See Exactly the Same Rainbow
Now we can answer the question at the start. Every raindrop bends and reflects sunlight in the same way, but only the light from some of them reaches your eye, and that light is your rainbow[3]. Your friend is standing in a slightly different spot, so a slightly different set of raindrops sends light to their eyes. NASA's Astronomy Picture of the Day, a daily space and sky photo feature, puts it plainly: no two observers can see exactly the same rainbow[6].
It also means you can never walk to the end of a rainbow. As you move, the set of drops that sends you light moves with you, so the bow seems to back away at the same pace. There is no pot of gold to find, because there is no place where the rainbow sits. Two people can point in the same direction, but each is looking at a rainbow that only they can see.
Test the Answer Yourself with a Garden Hose or Yard Sprinkler
- Make a rainbow with a garden hose. On a sunny morning or late afternoon, when the Sun is low, stand in your garden or yard with your back to the Sun and spray a fine mist in front of you. Fine droplets act like tiny raindrops. The National Weather Service says the Sun has to be less than 42 degrees above the horizon, so midday is a poor time to try[1]. Never look straight at the Sun, and ask an adult before using the hose.
- Compare rainbows with a friend. While the mist is in the air, stand side by side with a friend, each pointing at where the bow appears to touch a tree or a fence. Are your two spots the same? Then move a few steps and see what the rainbow does.
- Look for the dark band. After a real rain shower, if a double rainbow appears, check whether the sky between the two bows looks darker than the sky outside them.
- Read the original. Newton's account of his prism experiments is in the Royal Society's Philosophical Transactions from 1672. The Linda Hall Library page linked below is a friendly place to start. It is a US science library that shares short profiles of scientists.