The Physics Behind Post‑Rain Rainbows

Rainbows appear when sunlight encounters a collection of water droplets suspended in the atmosphere after a rain shower. Each droplet acts as a tiny spherical prism, refracting incoming solar rays as they enter the droplet, reflecting them once off the inner surface, and refracting them again as they exit. This combination of refraction, internal reflection, and a second refraction separates white sunlight into its constituent colors—red, orange, yellow, green, blue, indigo, and violet—producing the familiar multicolored arc.

The process begins with refraction, the bending of light as it passes from air (with a lower refractive index) into water (with a higher refractive index). Because the refractive index varies slightly with wavelength, shorter wavelengths (blue and violet) are bent more sharply than longer wavelengths (red). After entering the droplet, the light reflects off the back interior surface. This single internal reflection is essential; without it, the light would simply pass through the droplet and not return toward the observer.

A second refraction occurs when the reflected light exits the droplet back into the air. At this stage the dispersion created by the first refraction is amplified, widening the angular separation between colors. For the primary rainbow, the emergent rays are most intense at an angle of approximately 42 degrees from the line opposite the sun for red light and about 40 degrees for violet. The observer therefore sees a circular arc centered on the point opposite the sun, with red on the outer edge and violet on the inner edge.

Secondary rainbows can sometimes be observed outside the primary arc. These arise when light undergoes two internal reflections inside the droplet before exiting. The additional reflection reverses the order of colors, placing red on the inner edge and violet on the outer edge, and widens the angular radius to roughly 50–53 degrees. However, each successive reflection reduces the intensity of the light, making secondary and higher‑order rainbows fainter and more difficult to see.

Atmospheric conditions influence the clarity and visibility of rainbows. A broad distribution of droplet sizes yields a smoother, more continuous spectrum, while uniform droplet sizes can produce sharper, more vivid bands. The presence of sunlight behind the observer, low solar elevation, and a backdrop of darker clouds or a clear sky enhance contrast, allowing the rainbow to stand out. Because the phenomenon relies on geometric optics, the fundamental principles remain constant regardless of location, making rainbows a universal and recurring feature of post‑rain skies worldwide.