A double rainbow forms when sunlight bounces twice inside raindrops instead of once. Every raindrop that creates the familiar primary arc also sends a small amount of light through a second internal reflection, producing a larger, fainter arc above the first with its color order flipped. The two bows are always generated together, so in a sense every rainbow is a double rainbow; the second arc is just usually too dim for your eyes to pick out against the bright sky. When conditions are right, though, both arcs blaze into view, separated by a noticeably darker strip of sky that has its own name and its own explanation.
How the Primary Rainbow Forms
Sunlight enters a raindrop, slows down, and bends. That bending at the surface is refraction, and it is what separates white light into its component colors because each wavelength bends by a slightly different amount. Once inside the drop, the light hits the far inner wall and reflects back. On its way out through the front surface, it refracts again. The net effect is that light exits the drop at an angle of roughly 42 degrees relative to the incoming sunlight, fanned out into a spectrum. Red light bends the least and exits at the steepest angle, so it appears on the outer edge of the primary bow. Violet bends the most and sits on the inner edge.
You see a full arc because millions of raindrops are involved, each at a slightly different position in the sky. Only the drops that happen to be at the right geometric angle relative to your eye and the sun send their refracted light toward you. The result is a circle (or, from the ground, a semicircle) centered on the point directly opposite the sun from your perspective. The lower the sun sits in the sky, the more of the arc you can see, which is why late-afternoon and early-morning showers produce the tallest, most dramatic rainbows.
The Second Reflection That Creates the Outer Bow
Inside every raindrop, some of the light that hits the back wall does not escape on the first bounce. Instead it reflects a second time, rattling around inside the drop before finally exiting. This second internal reflection sends light out at a wider angle, roughly 51 degrees from the incoming sunlight rather than 42. That wider exit angle means the secondary bow appears higher in the sky, forming a larger arc that sits outside the primary one.
Each reflection inside the drop costs energy. Some light leaks out of the drop at every surface encounter instead of reflecting, so the twice-reflected beam that creates the secondary bow is substantially dimmer than the once-reflected beam of the primary bow. In practice, the secondary arc is roughly half as bright, and on hazy days or with light rain it can fade to invisibility. That is why double rainbows feel like special events even though the physics is always happening.
The extra reflection also reverses the color sequence. In the primary bow, red is on top and violet is on the bottom. In the secondary bow, violet is on top and red is on the bottom. This reversal is a direct geometric consequence of the light bouncing one more time before leaving the drop, which flips the order in which different wavelengths fan out.
Alexander’s Dark Band
If you look carefully at a double rainbow, the strip of sky between the two arcs appears distinctly darker than the sky above the secondary bow or below the primary bow. This region is called Alexander’s dark band, named after Alexander of Aphrodisias, who described it around 200 CE. The dark band is not an illusion or a contrast trick; it has a real optical cause.
Light that exits a raindrop after one internal reflection cannot scatter at angles between about 42 and 51 degrees. The primary bow concentrates light at its 42-degree edge, and the secondary bow concentrates light at its 51-degree edge, but the zone in between receives essentially no rainbow-scattered light from either process. Meanwhile, the sky below the primary bow gets a wash of extra light from all the rays that exit at angles less than 42 degrees, making that region subtly brighter. The result is a visible darkening in the gap between the two arcs.1Physics Reports. From Alexander of Aphrodisias to Young and Airy
When and Where Double Rainbows Are Easiest to See
You need three things: sunlight behind you, rain in front of you, and a sun that is not too high in the sky. When the sun is above about 42 degrees elevation, the primary bow drops below the horizon for a ground-level observer, and the secondary bow follows it down shortly after. That is why double rainbows are most common in the morning and evening hours, or at higher latitudes where the sun stays lower for longer portions of the day. From an airplane or a mountaintop, you can see the full circle of both bows because there is no ground cutting off the lower half.
Rain intensity matters, too. A heavy, localized shower with large drops against a dark background tends to produce the most vivid double rainbows. Large drops create brighter, more sharply defined arcs because they keep their roughly spherical shape, which concentrates the outgoing light more precisely. Very small drops, on the other hand, spread the light over a broader angle and wash out the colors.
Raindrop Shape and Why It Matters
Raindrops are not teardrop-shaped. Small ones are nearly perfect spheres, but as they grow larger, air resistance flattens them into something more like a hamburger bun. This flattening affects the rainbow in subtle but visible ways. Slightly oblate drops can enhance the visibility of fine interference fringes near the top of the bow while weakening them at the sides. In more extreme cases, the distorted shape splits the primary arc into two overlapping bows, producing a branching pattern called a twinned rainbow.2Applied Optics. Light scattering from sessile water drops and raindrop-shaped glass beads as a validation tool for rainbow simulations
Twinned rainbows look nothing like a standard double rainbow. Instead of a second, wider arc above the first, a twinned rainbow shows two primary bows that diverge from each other at some point along the arc, often near the top. The split happens because large, flattened drops and small, spherical drops in the same rain shower bend light to slightly different angles. When a mix of drop sizes is falling at once, you can get these odd branching patterns that even experienced sky watchers sometimes mistake for something else entirely.
Beyond Double: Third, Fourth, and Higher-Order Rainbows
If one extra internal reflection produces a secondary bow, it stands to reason that two extra reflections could produce a third, three a fourth, and so on. These higher-order rainbows do exist, but they get progressively dimmer with each added reflection because more light escapes the drop at every bounce. The third-order and fourth-order rainbows are also awkwardly positioned: they appear around the sun rather than opposite it, which means you would need to look toward the sun and past the glare of direct sunlight to see them. For centuries, these bows were considered purely theoretical.
That changed in 2011, when photographers using careful image-stacking techniques captured what appear to be the third and fourth-order natural rainbows for the first time. By 2013, the same approach had pushed the limit further. A team working near Magdalena, New Mexico, produced a contrast-enhanced stack of 12 digital photographs that showed color bands at the correct position and in the correct order for a seventh-order rainbow, sitting about 64 degrees from the sun.3Optica Publishing Group (Applied Optics). Probable photographic detection of the natural seventh-order rainbow No human eye could have picked this out in real time; it took digital stacking and enhancement to pull the signal from the background sky. In laboratory settings, using a single suspended water drop and a spectrometer, researchers have observed up to the 13th-order rainbow in water and even the 17th-order rainbow in drops of light corn syrup, which has a different refractive index that shifts the bow positions.4American Journal of Physics. Multiple rainbows from single drops of water and other liquids
The practical takeaway for casual sky watchers is that the secondary bow is the highest-order rainbow you are likely to see with the naked eye. Third-order and above require either digital processing or controlled lab conditions.
Supernumerary Bows
Sometimes, just inside the primary arc, you can spot a series of faint pastel-colored fringes, often greenish or pinkish, that do not match the standard color sequence. These are supernumerary bows, and they form through a completely different mechanism than the primary and secondary arcs. Two rays of light can enter the same raindrop, follow slightly different paths inside it, and exit at the same angle. When those two rays recombine, they interfere with each other. If their wave crests align, the light is reinforced; if the crests and troughs cancel out, the light dims. The resulting pattern of bright and dark fringes is what you see as supernumerary arcs.5PubMed. Supernumerary arcs of rainbows: Young’s theory of interference
Supernumerary bows show up most clearly when the raindrops are small and uniform in size. If the drops vary a lot, the interference fringes from different-sized drops land at slightly different angles and smear each other out. This is why you see supernumerary arcs most often in fine, uniform drizzle or mist, and almost never in heavy, chaotic thunderstorms. The fringes tend to be most visible near the top of the bow, partly because the spherical shape of small drops is most consistent at the apex and partly because the flattening of larger drops disrupts the precise geometry needed for clean interference.1Physics Reports. From Alexander of Aphrodisias to Young and Airy
Fogbows and What Happens When Drops Get Very Small
Shrink the water drops far enough and the rainbow loses its color altogether. In fog, the droplets can be as small as 10 micrometers across, roughly a tenth the diameter of a typical raindrop. At that size, the color-separating effect of refraction gets overwhelmed by diffraction, which spreads each wavelength over a wide angle and mixes the colors back together. The result is a fogbow: a broad, ghostly white arc in roughly the same position as a normal rainbow, sometimes with just a faint reddish tint on the outer edge and a bluish tint on the inner edge.6Journal of Quantitative Spectroscopy and Radiative Transfer. Simulation of rainbows, coronas and glories using Mie theory and the Debye series
Fogbows can also produce secondary arcs, though these are even harder to spot than a secondary rainbow since the whole structure is pale and washed out. You are most likely to see a fogbow from a hilltop or a ship at sea, anywhere fog forms with the sun low behind you. Mountain climbers sometimes see a related phenomenon called a glory, where a small, colorful ring appears around the shadow of their own head on a cloud bank below, but glories involve a different scattering mechanism and are not actually rainbows.
Reflected and Reflection Rainbows
Bodies of water add their own complications. A reflected rainbow is the mirror image of a normal rainbow seen in a calm lake or pond: the arc appears to curve downward from the water surface, and its colors and geometry are simply a reflection of the bow in the sky above. But a reflection rainbow is different. This one forms when sunlight bounces off a body of water before entering the raindrops, effectively creating a second light source below the horizon. The resulting arc sits higher in the sky than the normal primary bow, and the two arcs can cross each other. In rare conditions, observers have reported seeing the reflected versions of both the primary and secondary bows simultaneously, along with Alexander’s dark band reproduced in the reflection.7Nature. Rainbow Reflected from Water
This can make a lakeside rainbow scene look surreal: four or more arcs in the sky, some crossing, some inverted, all produced by the same physics of refraction and reflection but from different source geometries. These multi-arc displays are genuinely rare because they require a large, mirror-flat water surface, low sun, and a rain curtain in the right position all at once.
Polarization of Rainbow Light
Rainbow light is strongly polarized, meaning the light waves vibrate predominantly in one direction rather than randomly. If you look at a rainbow through polarized sunglasses and rotate them, the bow will brighten and dim dramatically as the filter aligns with or opposes the polarization direction. The primary bow is strongly polarized tangentially along the arc, and the secondary bow is polarized as well. Higher-order bows, from the third order upward, are polarized to a degree between about 75 and 78 percent.8Applied Optics. Polarization and visibility of higher-order rainbows
This polarization is not just a curiosity. It is the reason rainbow photography sometimes looks oddly different from what you remember seeing with the naked eye. A camera’s UV filter or a polarizing filter can either enhance or suppress the bow depending on its orientation. If you have ever taken a photo of a rainbow and found that part of the arc vanished, the culprit was likely a circular polarizer on your lens cutting out the polarized light at certain angles.
Rainbows as Clues to Other Worlds
The same physics that creates rainbows on Earth could, in principle, produce them on any world with liquid droplets in its atmosphere and a star to illuminate them. Astrobiologists have explored this idea as a way to detect liquid water on distant exoplanets. Because liquid droplets produce a distinctive spike in polarized light at the rainbow scattering angle, while solid particles like ice crystals and dust do not, looking for that polarization signature in the light reflected from an exoplanet could reveal whether its clouds contain liquid drops. The refractive index of the liquid determines the exact angle of the spike, so comparing the observed angle against known values could even identify the liquid involved.9PubMed. Rainbows, polarization, and the search for habitable planets
No telescope has yet detected a rainbow signature on an exoplanet; current instruments lack the sensitivity. But the concept is sound enough that it has been proposed as a target for next-generation space observatories. If a planet’s reflected starlight shows a clean polarization peak at the right scattering angle, that would be strong evidence for liquid droplets in its atmosphere, something no other remote-sensing technique can distinguish as cleanly from ice or mineral particles. On a world where the liquid happens to be water, that peak would land at around the same angle as an earthly rainbow.
Common Misconceptions About Double Rainbows
One persistent idea is that the second arc is a “reflection” of the first, as if the sky were acting like a mirror. It is not. Both bows are independently generated inside every raindrop; the secondary bow is not a copy of the primary but a separate optical path involving an additional internal reflection. Another common mistake is thinking that double rainbows are rare. The secondary bow is always being produced whenever you see a primary bow. What varies is whether conditions are bright and clear enough for the dimmer outer arc to be visible against the background sky.
People also sometimes confuse twinned rainbows with double rainbows. A twinned rainbow shows two primary arcs that split apart from each other, often near the top of the bow, while a true double rainbow consists of a primary and a secondary arc separated by Alexander’s dark band with reversed color sequences. The causes are entirely different: twinning results from a mix of raindrop sizes and shapes, while the secondary bow results from an extra bounce of light inside every drop regardless of shape.
Finally, there is the viral “double rainbow” excitement suggesting these displays are mysterious or unexplained. The optics have been well understood for centuries. Descartes worked out the geometry of both the primary and secondary bows in the 1630s, and Newton added the explanation for why the colors separate. What modern research has refined is the fine detail: how non-spherical drop shapes create twinning, how interference produces supernumerary fringes, and how digital photography has revealed higher-order bows that no previous generation could have detected. The basic answer to why double rainbows happen, though, has been settled science for nearly 400 years.