The cone and the horizon

Why only half a circle?

Join every direction 42° from the shadow point and you get a cone with its tip at your eye. Where the cone meets the sky, it makes a circle, and that circle is the rainbow. But the shadow point is below the horizon, so the ground hides the bottom of the circle. That is why a rainbow looks like an arch.

Why?The higher the Sun climbs, the lower the shadow point sinks, and the rainbow sinks with it. Once the Sun is higher than about 42°, the whole rainbow drops below the horizon. That is why rainbows from the ground are most often seen in the morning or late afternoon.

Learn moreWhen the Sun sits right on the horizon (0° high), the shadow point is on the horizon too, and the rainbow is an exact half circle. That is when a rainbow looks tallest and biggest. Use the slider below to change the height of the Sun.

Height of the rainbow’s top

27°

Top of the rainbow

42° minus the Sun’s height

Rainbow hides when the Sun is

higher than about 42°

calculated from the refractive index of water (IAPWS, 20 °C) and the laws of refraction and reflection