Why does a rainbow always curve, and could you ever reach its end?
After you watchWhy does a rainbow always curve, and could you ever reach its end?
The short answer
A rainbow curves because it is really a circle of raindrops that all sit at one special angle — about 42 degrees — from the point directly opposite the sun, which is the center of your own shadow. Only drops at that angle can bounce sunlight back to your eye as split colors, and that set of drops traces a circle. You can never reach a rainbow's end, because the bow is tied to where you stand: step sideways and the whole thing slides along with you.
Try this next
- What if you fill the sky with raindrops but then move the sun lower toward the horizon? In the explainer, change where the light comes from and predict first: does the center of the bow (opposite the sun) rise or sink? Watch whether more of the circle peeks above the ground.
- What if the special angle were bigger than 42 degrees instead of exactly 42? Predict how the size of the bow would change, then look for the faint second rainbow at about 51 degrees and check if it really is a wider circle.
Now you — bend it
- What if What if you slide the sunbeam right to the very edge of the drop versus straight through its middle — where does the exit angle pile up?Drag the 'where the sunbeam hits the drop' slider slowly from MIDDLE out toward an EDGE and watch the angle readout. Predict where many nearby slider positions all leave at almost the SAME angle (it crowds near about 42° and barely moves there) versus where it races away. That crowding is exactly why the bow has a bright edge instead of a smooth fade.
- What if Thought experiment (no slider for this): what if you flipped the sky rule to 'any angle' AND took a step at the same time?First flip to the made-up 'any angle' rule and press 'Take a step sideways': there is no crisp bow to follow, just a smear. Now flip back to the real 'one fixed angle' rule and step again — the bow snaps back and slides with you. Predict before each step whether a shape will track you, then watch which rule actually makes the bow belong to you.
- What if Thought experiment (no slider for this): what if the raindrops were made of something that bends light MORE than water — like syrup or diamond?There's no fluid control to turn, so reason from the one-drop slider as a stand-in: the angle it crowds toward (about 42°) is set by how sharply water turns the ray. Predict which way that pile-up angle — and so the whole bow's radius — would move if the drops bent light harder, and whether your rainbow would still match everyone else's.
Can you prove it?A rainbow's angular radius (~42 degrees) is fixed by the water itself, not by the sun, the rain, or where you stand — which is why every rainbow on Earth is the same size. — Drive the one-drop slider ('where the sunbeam hits the drop') from TOP EDGE through MIDDLE to BOTTOM EDGE and watch the angle readout: the exit angle crowds up near about 42 degrees and refuses to climb past it, no matter where the beam hits — it 'piles up' at that ceiling. Then flip the sky's rule to 'one fixed angle' and press 'Take a step sideways': the bow keeps the very same shape and size as it slides with you, showing the angle doesn't depend on where you stand. Test the consequence outdoors: measure a real bow's radius with a fist held at arm's length (about 10 degrees wide) on two different days — it should read the same four-fists-wide arc every time.
Design your own test:Before you drag it: predict where on the slider the exit-angle readout barely changes (rays piling up at almost the same angle) and where it changes fastest. Then slide it slowly across and watch the angle to see if you guessed the pile-up spot near 42°.
Explain it to a 6-year-old: A rainbow is a circle of raindrops that all sit the same special distance from the shadow of your head, so it always curves and always slides away when you chase it.
The whole story
How it works
Sunlight goes into a round raindrop, bends, bounces once off the back of the drop, and bends again on the way out, splitting white light into its colors. Because of the drop's round shape, those bounced-back colors always leave near one special angle, about 42 degrees, measured from the point straight opposite the sun (the center of your shadow). So the only drops that can send their colors to your eye are the ones sitting at that angle around your shadow. Those drops form a ring, which is why a rainbow is always a curve. The ground hides the bottom of the ring, so from the ground you usually see just the top arc.
What people get wrong
Many people think a rainbow is a real object parked in one spot, so you could run to where it touches the ground and find the end. But a rainbow is not in a fixed place at all. It is simply the set of raindrops at one special angle from your own eye, centered on your shadow. Because it depends on where you stand, it moves when you move, two people never see exactly the same rainbow, and its end is always one step further away.
The catch
The fixed-angle rule is exactly what makes the bow crisp and curved, but it also means the rainbow belongs to you and only you: it is centered on your shadow, so it slides along when you move and the person next to you is seeing a slightly different bow. The lit drops truly make a full circle, but from the ground the horizon hides the bottom half because there are no raindrops below it, so you see only the top arc — though from a plane or in the spray of a waterfall you can sometimes catch the whole circle.
Questions kids ask
Why can't you ever reach the end of a rainbow?
Because a rainbow is not sitting in one place. It is the ring of raindrops at one special angle from your own eye, centered on your shadow. When you walk toward it, the bow simply moves with you to stay at that angle, so its end is always the same distance away and you can never catch it.
Is a rainbow really a full circle?
Yes. The lit raindrops form a complete circle around the point opposite the sun. From the ground the horizon hides the bottom half, because there are no raindrops below it to light up, so you only see the top arc. From an airplane or in the mist of a waterfall, you can sometimes see the entire circle.
Why is the special angle about 42 degrees?
When sunlight bounces once inside a round raindrop, the rays bunch up and come back out near one angle, about 42 degrees from the point opposite the sun. That bunching is set by the drop's round shape and how much light bends in water, and it is the same for every drop, which is why every rainbow has the same size.
Why does red always sit on the outside of the bow?
Each color bends by a slightly different amount inside the drop, so they leave at slightly different angles. Red comes out at about 42 degrees and violet at about 40 degrees, so red lands on the outer edge of the arc and violet on the inner edge, with the other colors in between.
Talk about it
- Guess first: if you and I both look at the same rainbow, are we seeing the exact same one? Why or why not?
- Where do you think the center of a rainbow is? Try pointing at it before we figure it out together.
- Why might you never be able to walk to the end of a rainbow, no matter how fast you run?
For grown-ups
Sunlight refracts entering a spherical droplet, reflects once off the back, and refracts again on exit. Dispersion makes each wavelength leave at a slightly different angle, and the rays pile up at a minimum-deviation angle, producing a bright caustic about 42 degrees from the antisolar point (red near 42 degrees, violet near 40 degrees). Every droplet at that angular radius around the antisolar point contributes, so the locus of lit drops is a circle, seen as an arc because the horizon cuts it off. The bow is observer-centric, which is why it tracks the viewer and has no reachable end. A fainter secondary bow, from two internal reflections, appears around 51 degrees with the colors reversed.
Keep going
What else makes you wonder?
- If the rainbow is centered on your shadow, what happens to it on a really tall mountain or from a plane window?
- Why does the secondary rainbow that sometimes hangs above the bright one have its colors flipped?
- Could there be rainbows on other worlds, where the rain is made of something other than water?