Why Are a Double Rainbow's Outer Colors Reversed?

The fainter arc outside a bright rainbow is not a copied image of the first arc. It is a secondary rainbow formed by sunlight that reflects twice inside raindrops before reaching your eyes. Light that reflects once produces the primary rainbow. The extra reflection sends the returning colors along a different path, so the secondary arc appears farther out and its color order is reversed. Those two visible differences are clues to what happened inside the drops.

Start with the usual viewing arrangement: the Sun is behind the observer and raindrops are in the sky ahead. As sunlight enters a drop, it bends at the air-water boundary, and its different wavelengths bend by slightly different amounts. Some of the light reflects from the inside back surface of the drop. It bends again as it leaves. Many drops at the appropriate angles send particular colors toward the same observer, making the familiar primary bow. The bow is not a colored object hanging at one fixed location in the sky; it depends on the positions of the Sun, droplets, and viewer.

Not every ray follows that one-reflection route. Some light reflects a second time inside a drop before escaping. The U.S. National Oceanic and Atmospheric Administration and the National Weather Service both identify this second internal reflection as the source of the secondary bow. Because the path through the drop is different, the returning rays reach an observer from a different range of directions. This puts the secondary rainbow outside the primary one rather than directly on top of it. You can see the two paths at work without needing two separate rain showers or a second Sun.

The colors provide an especially useful check. In the primary rainbow, red lies on the outer side of the arc and violet on the inner side. In a secondary rainbow, red lies on the inner side and violet on the outer side. The colors of sunlight have not changed, and the rain has not somehow sorted itself into two kinds of drops. The extra reflection changes the relationship between each wavelength's exit direction and the observer's line of sight. The color sequence that the observer receives across the arc therefore flips.

Why is the second arc usually harder to see? A ray does not keep all its light through every encounter with a drop's boundary. Some light leaves the path at each opportunity instead of continuing to reflect toward the observer. The twice-reflected route delivers less light to the eye than the primary route, making the outer arc fainter. Background conditions matter as well. Against a bright or uneven sky, the secondary bow may be present yet difficult to distinguish, even when the primary bow is obvious.

There can also be a darker strip of sky between the two bows. Called Alexander's dark band, it appears because comparatively little light from the main rainbow paths reaches the viewer from directions between the primary and secondary arcs. It is not a dark substance between layers of rain. The effect becomes easier to notice when both arcs are clear, but cloud cover and lighting can alter the actual brightness across the sky. The band, like the arcs themselves, is an optical result of where the redirected sunlight reaches an observer.

Each observer also has a particular geometry. Drops in different parts of the sky send different colors to one pair of eyes, and a person standing elsewhere receives light from a different collection of drops. The bows look stable because there are so many droplets, not because two painted arches occupy fixed positions in the air.

A double rainbow is thus one set of raindrops revealing two routes for sunlight. One internal reflection builds the brighter inner bow; two build the weaker outer bow. The extra turn changes both where the colors appear and which color sits on which side. If you see two arcs after a shower, look for the reversed color order and the darker region between them. Those details show why the second bow is a separate optical path rather than a pale enlargement of the first.