Why are rainbows curved?

The answer

A rainbow is a circle of light centered on the antisolar point (the point directly opposite the Sun from your perspective). Sunlight enters raindrops, refracts, reflects off the back surface, and refracts again on exit, separating into colors at a consistent angle of about 42 degrees from the antisolar point. Since this geometry traces a cone around that point, you see an arc. From an airplane, you can sometimes see a complete circular rainbow because the ground doesn't block the lower half.