Why are the colors reversed in a double rainbow?
The outer, secondary arc in a double rainbow is produced by light that reflects twice inside water droplets. This path differs from the single internal reflection forming the primary bow and reverses the angular sequence of colors. Red consequently appears nearer the inside edge of the secondary bow, with violet nearer its outer edge.
Mechanism and everyday examples
1. How does light travel through the primary bow? Sunlight refracts when entering a roughly spherical water droplet, reflects once internally, and refracts again on leaving. Different wavelengths deviate by different amounts, concentrating the components of white light in different directions. The Sun behind the observer and the rain ahead must have suitable geometry. The primary bow has red outside and violet inside; one droplet does not send every color into your eye along the same direction. 2. Why does an extra reflection reverse the order? Light forming the secondary bow undergoes two internal reflections. That additional turn concentrates emerging rays at different angles and reverses their color order. The secondary bow is outside the primary one. The pair is not simply a single rainbow duplicated by a camera: it consists of two angular concentrations associated with different light paths. Droplet shape and size can influence the details and definition of both arcs. 3. Why is the outer bow fainter? At each interaction with a droplet boundary, light is divided among different paths. An extra reflection and distribution across a wider range of angles reduce the brightness reaching the observer in the secondary bow. Suitable contrast with the surrounding sky helps make it visible. Clouds obscuring the Sun or changes in the rain region can affect the arcs differently. Two bows should not be expected to have equal brightness in every double rainbow.
Observation, applications and misconceptions
4. Why can the space between them look dark? The darker region between the primary and secondary bows is called Alexander's dark band. Fewer rays emerge from droplets toward some of those viewing angles, reducing the brightness compared with neighboring areas. The band is not completely devoid of light; atmospheric scattering and other contributions remain. Darkness here is a relative brightness difference rather than absolute absence. Photograph processing may exaggerate that contrast beyond the appearance seen directly. 5. Can you move closer to a rainbow? The arc's position depends on the observer's viewing direction. Walking changes which droplets send light to your eye at the required angles; it does not bring you closer to a fixed colored arch standing on the ground. Two people may see similar bows without receiving light from exactly the same droplets. From sufficiently high viewpoints, droplets can fill enough of the view to reveal a full circle; from the ground, the horizon usually hides the lower portion. 6. How can other colored arcs be confused with it? Fine additional stripes inside the primary bow may be supernumerary arcs associated with wave interference. They differ from the secondary bow formed by two internal reflections. Ice halos around the Sun also have a different position and mechanism. Identification requires noting whether the arc lies opposite or around the Sun, which bow is outside, and the color sequence. Rainbow viewing does not require looking at the Sun; keep it behind you. The outer bow's larger angular radius does not mean that droplets have formed a physically larger arch in space; the observation concerns the directions in which light emerges.