Why Is a Rainbow Arc-Shaped?
A rainbow is not an object in space but a cross-section of a 42° cone centered on the observer. That is why it is an arc, why it moves with you, and why your neighbor sees a different rainbow.
You've seen a rainbow after rain. It's always arc-shaped.
But why is it always an arc? Could it be a straight line? A full circle?
And where exactly is the rainbow? Can we reach it if we walk toward it?
The common answer: "rainbows are arc-shaped because sunlight gets prism-split through rain" — or "raindrops are arranged in an arc." Sounds plausible. But this isn't the real essence.
Actually, a rainbow is nowhere in space. A rainbow = a cross-section of a 42° cone centered on the observer.
When sunlight enters a water droplet: refraction (entering) → reflection (off the back of the droplet) → refraction (exiting). Each wavelength (color) bends slightly differently → dispersion. Red returns to the observer at about 42°. Violet returns at about 40°. All rainbow colors appear at angles between these.
But why an arc? The center of the rainbow cone is directly opposite the sun from the observer (anti-solar point). All droplets sitting on the 42° cone around this center send rainbow light to the observer. When this cone is cut by the horizon → an arc (half-circle). From an airplane or inside waterfall mist, there's no horizon → full-circle rainbow.
→ A rainbow is not an object in space — it's an optical phenomenon defined by the observer. The rainbow your neighbor sees is actually a different rainbow (their 42° cone is positioned differently). The reason you can't reach a rainbow — it moves with you.
The diagram below walks through the sun–droplet–observer relationship in stages. ① Sunlight enters the droplet and splits into seven colors via refract→reflect→refract. ② Red returns to the observer at about 42° (the red 42° callout). ③ A 42° cone centered on the anti-solar point is revealed. ④ The horizon cuts that cone into an arc-shaped rainbow. Drag the observer (↔) left and right and the rainbow moves with you — which is why you can never reach its end — and press "Airplane View" to remove the horizon and see a full circle.
Step through with the buttons (1·2·3·4). Drag the observer (↔) and the rainbow follows; "Airplane View" reveals the full circle.
[Rainbows from an airplane] From a plane, rainbows appear as complete circles, because no horizon cuts the cone. Same inside waterfall mist.
[The legend of gold at the rainbow's end] The classic legend says gold lies at the rainbow's end. But rainbows have no position — they move with you. You can never reach the end of a rainbow.
[Double rainbows] The second, fainter rainbow above the main one is from light that reflected twice inside droplets (51° angle). It's outside the primary, and its colors are reversed (red on the inside).
[Same place, different person = different rainbow] The rainbow your friend sees next to you is literally a different rainbow — each observer has their own 42° cone. Two people can never photograph exactly the same rainbow.