What They (Probably) Don't Teach You About Rainbows At School

Rainbows aren’t just “light refracting and reflecting.” They form because raindrops act like tiny optical devices that concentrate different colors at specific angles, producing a colored ring that only becomes visible from a particular viewpoint. The core insight is that each raindrop sends back a cone of light whose color depends on the maximum scattering angle—set by geometry, refraction, and the wavelength-dependent response of light in water or glass. That angle is about 42° for red light in water, which is why rainbows appear as an arch centered on the antisolar point (your shadow). This matters because it replaces memorized rules with a mechanism that also predicts the “weird” details people notice in real life: why the sky above a rainbow looks darker, why sunglasses can erase it, and why double rainbows and faint extra bands appear.

The explanation starts with a single raindrop modeled as a sphere. Light from the sun enters the sphere, refracts according to Snell’s law, and then some of it reflects off the back surface. As the incoming ray hits the sphere at different heights (impact parameters), the outgoing reflected ray reaches a maximum deflection angle and then turns back. That turning point creates a caustic: a concentration of light rays at a particular angle. Because different colors bend differently—shorter wavelengths (blue) produce larger phase effects in the material and therefore different maximum scattering angles—the caustic angle shifts with color. When many raindrops contribute these color-specific caustics toward an observer, the result is the familiar rainbow ring.

The arch geometry follows directly from viewing conditions. For a given color (like red), the observer sees light only when the sun–raindrop–eye angle matches the caustic angle (about 42° for red). Violet light from the same raindrops misses the eye, but raindrops slightly higher or lower in the sky send violet toward the observer at a shallower angle (around 40°). With raindrops everywhere, the full spectrum fills the arc between those angles. Because the center of the rainbow lies on the line from the sun through the observer’s head, each person sees a different rainbow; even the left and right eyes don’t necessarily receive identical sets of droplets.

Several classic “exceptions” become predictable once polarization and higher-order reflections enter the picture. Rainbow light is polarized because the relevant back-reflection happens near Brewster’s angle, where one polarization component transmits through the droplet and the other reflects—so polarizing sunglasses can block the rainbow while leaving much of the rest of the scene visible. The region below the rainbow can look brighter because raindrops beneath the arc reflect light toward the observer, while drops above the arc do not. Double rainbows arise from additional internal reflections inside droplets; between the primary and secondary deflection ranges lies Alexander’s Dark Band, where neither once- nor twice-reflected light reaches the observer.

Finally, the video connects faint, closely spaced bands and “glories” to interference. Supernumerary rainbows appear when raindrops are small enough (fractions of a millimeter) that rays from slightly different parts of the droplet arrive with path differences on the order of a wavelength, creating alternating bright and dark fringes. Glories (Brocken bows) are similar but occur around the observer’s shadow with much smaller angular radii (about 2–4°), again driven by interference from tiny droplets in fog or clouds. That interference pattern later inspired CTR Wilson’s cloud chamber, beginning with his observation of colored rings around a shadow in mist.