A Rainbow Is Actually a Full Circle

A rainbow is naturally arranged as a circle, although observers on the ground usually see only an arc. The circle is centered on the antisolar point, the direction exactly opposite the Sun from the observer. Every suitable raindrop that sends light toward the eye at the required angle contributes one point to that geometry.

Sunlight entering a raindrop bends because its speed changes, separates by wavelength, reflects from the inside of the drop and bends again as it leaves. For the primary rainbow, the strongest returning light reaches the observer at an angle of roughly 40 to 42 degrees from the antisolar direction, with red on the outer edge and violet toward the inside.

Rotating that angle around the line from the Sun through the observer produces a cone of possible rays. The eye sees the cone projected against distant rain as a circle. There is no colored hoop sitting at one fixed location in the landscape; the bow depends on the observer's position, so two people receive light from different droplets.

The ground normally blocks the droplets that would form the lower part of the circle. When the Sun is low, a large arc rises above the horizon. From an aircraft, mountain or other high viewpoint, droplets may lie below the observer as well as ahead, making a complete circle—or much more of one—visible.

A secondary rainbow forms when light reflects twice inside droplets. It appears outside the primary bow, is fainter and has its color order reversed. Other effects, including supernumerary bands and pale fogbows, show that wave interference and droplet size can add detail beyond the simplest ray diagram.

The familiar arch is therefore a horizon-limited view of a three-dimensional optical arrangement. A rainbow follows the observer and the antisolar point, not a place where treasure could be reached. Height does not create the missing half; it simply removes the obstruction that usually hides it.