A rainbow is a spectacular optical and meteorological phenomenon resulting from the complex interplay between sunlight and water droplets suspended in the atmosphere. For a rainbow to appear, an observer must have the sun positioned directly behind them, illuminating airborne water droplets, such as rain or mist, in front of them. This arrangement of light source, droplet, and viewer is necessary to capture the light scattered back toward the eye. While the single colorful arc is the most recognized form, a deeper look into the physics of light reveals that the number of possible rainbows extends far beyond this familiar sight.
The Anatomy of the Standard Primary Rainbow
The most common and brightly visible arc is the primary rainbow, forming through a precise sequence of events within individual spherical water droplets. When sunlight enters a droplet, it first undergoes refraction and dispersion, separating the white light into its constituent colors.
The light then travels to the back inner surface for a single internal reflection. As the light exits the droplet, it refracts a second time, further amplifying the color separation. This single reflection concentrates the light at a viewing angle of approximately 42 degrees from the anti-solar point (the point directly opposite the sun). The primary rainbow always displays a fixed color order, with red on the outer edge and violet on the inner edge.
The Creation of Multiple Rainbows
The number of possible rainbows is determined by how many times light reflects inside the water droplet before exiting. The secondary rainbow, seen arcing wider and fainter outside the primary, is created by light undergoing two internal reflections. This extra reflection causes a significant loss of light intensity, making the secondary arc noticeably dimmer.
The double reflection reverses the color sequence, placing violet on the outer edge and red on the inner edge, contrasting the primary bow. This secondary arc appears at a wider angle, around 50 to 53 degrees, and the space between the two bows often appears darker due to Alexander’s band.
Moving beyond the secondary, tertiary (three reflections) and quaternary (four reflections) rainbows are possible. These higher-order bows are exceedingly rare because light intensity diminishes drastically with each reflection. They are predicted to appear in the direction of the sun, making them difficult to isolate against the bright sky and are primarily confirmed through specialized photography or laboratory conditions.
Environmental Variations and Specialized Arcs
The appearance of a rainbow can be altered by environmental conditions, creating several specialized arcs. Moonbows are formed by moonlight, but the underlying physics of refraction and reflection remains the same. Since moonlight is significantly less intense than direct sunlight, the colors are often too faint to stimulate the color-sensitive cones in the human eye, causing the arc to appear white or monochromatic.
Fogbows occur when the atmosphere contains extremely small water droplets, such as those found in fog or mist. These minute droplets, typically smaller than 0.05 millimeters, do not separate the colors of light as effectively as larger raindrops. The result is a broad, often colorless or “ghostly” white arc, sometimes called a white rainbow.
Supernumerary arcs are faint, repetitive bands of pastel colors that appear just inside the primary rainbow, and occasionally outside the secondary. These are not caused by additional internal reflections but by the wave nature of light, specifically a phenomenon called interference. When light rays follow slightly different paths within water droplets of nearly uniform size, they interfere with one another, creating these delicate, repeating color fringes.
The Physical and Observable Limits
The theoretical number of possible rainbows is infinite, as there is no physical limit to internal reflections within a water droplet. However, the practical and observable limit is far lower due to the rapid loss of light intensity with each subsequent reflection. Approximately 90% of the light is lost after the second reflection, meaning the tertiary rainbow is only about 3% as bright as the primary.
This rapid decay in brightness makes it virtually impossible to see any rainbow beyond the secondary without specific tools or conditions. The highest number ever reliably confirmed and photographed in nature is the quaternary, or fourth-order, rainbow. Therefore, the observable reality for a human viewer under normal conditions is typically limited to the primary and secondary arcs.