Why Is a Rainbow Arc-Shaped?

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.

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.

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.

Rainbows from an airplaneFrom 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 endThe 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 rainbowsThe 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 rainbowThe 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.