Are There Triple Rainbows and How Do They Form?

Triple rainbows are real, but seeing one with the naked eye is so difficult that for centuries scientists debated whether it was even possible in natural conditions. The third-order rainbow, as physicists call it, forms when sunlight bounces three times inside a raindrop before exiting. That extra internal reflection sends the light toward the sun rather than away from it, which is the core reason you have almost certainly never noticed one: you would have to face into blinding sunlight and glare to spot it. The first confirmed photograph of a natural triple rainbow was not published until 2011, and extracting the rainbow from that image required digital processing because it was invisible to the unaided eye in the original photo.

How a Third Reflection Creates a Third Rainbow

Every rainbow starts the same way. Sunlight enters a raindrop, slows down and bends at the surface, reflects off the back wall of the drop, and bends again on its way out. That single internal reflection produces the bright primary rainbow you see arching across the sky opposite the sun. Some of the light reflects a second time before leaving the drop, producing the fainter secondary rainbow that appears above the primary, with its color order reversed. The tertiary rainbow is simply what happens when a small fraction of the light reflects a third time inside the drop before escaping.

Each reflection costs energy. The drop’s interior surface is not a perfect mirror, so a portion of the light passes through and is lost with every bounce. By the third reflection, the outgoing ray is dramatically weaker than the primary. That alone would make the triple rainbow faint. But the bigger problem is geometry. The angles at which light exits after three reflections direct it back toward the sun’s side of the sky, roughly 40 to 42 degrees from the sun itself. The primary and secondary bows sit on the opposite side of the sky from the sun, where the background is relatively dark rain clouds. The tertiary rainbow has to compete with the brightest part of the sky.

Why You Have Probably Never Seen One

The challenge is not just faintness. It is faintness layered on top of extreme glare. Forward-scattered sunlight from millions of raindrops floods the sunward sky with a bright, washed-out haze. The tertiary rainbow’s colors are embedded in that haze, producing almost no contrast against the background. Researchers who modeled the visibility of the natural tertiary found that it is “just visible” only under unusual combinations of lighting conditions and raindrop size distributions, such as when a very dark cloud sits directly behind the arc while the sun remains unobstructed.¹ In ordinary rainstorms, those conditions almost never line up.

That modeling work used several approaches to calculate what a human observer could actually perceive: the chromaticity (how saturated the colors would appear), the luminance contrast (how much brighter or darker the bow would be compared with the sky around it), and the color contrast. All three measures confirmed the same conclusion. Under most real-world skies, the tertiary rainbow falls below the threshold of human vision. It exists physically, casting its photons toward your eyes, but your visual system cannot pull the signal out of the noise.

Throughout history, a handful of observers claimed to have glimpsed a third rainbow, but those reports were scattered, unverified, and easy to dismiss. Some atmospheric scientists assumed tertiaries were inherently invisible in nature. That assumption held for a long time.

The First Photograph and How It Was Found

In 2011, a team of researchers reported the first likely photographic observation of a tertiary rainbow caused by sunlight in open air. The key word is “likely” because the rainbow was not visible in the original photograph at all. It was only after applying image processing techniques to a digital photo taken during a rainstorm that a faint arc emerged at the angular position and color dispersion predicted by theory.²

The researchers were meticulous about ruling out artifacts. Digital cameras can produce spurious color bands from lens flare, sensor reflections, or compression artifacts, any of which could mimic a faint arc of color. To confirm the finding, they carefully calibrated the image so that the angular position of the arc could be compared against the theoretically predicted radius from the sun. They also checked the dispersion pattern, meaning the spread and ordering of colors across the width of the arc. Both matched the theoretical prediction for a third-order rainbow, and the arc appeared where no known optical artifact would sit. Prior to this, there were no reliable photographs of the phenomenon. Only sparse visual reports existed in the literature.²

The technique that made this possible is straightforward in concept. A digital camera sensor records far more dynamic range than the human eye can perceive in a single glance, especially in the blue and green channels where the tertiary rainbow’s signal is strongest. By subtracting the smoothly varying background brightness (the sunlit haze), amplifying the residual signal, and enhancing color contrast, the researchers effectively did what your retina cannot: isolate a faint color pattern from an overwhelming wash of white light.

Fourth-Order and Fifth-Order Rainbows Exist Too

The discovery of the tertiary rainbow photograph opened the floodgates. In the same year, another team reported what is believed to be the first photographic recording of a quaternary (fourth-order) rainbow in nature. It appeared on the sun side of the sky with its red arc at a radius of about 45 degrees from the sun. The original pictures were subjected to various forms of image processing to reveal both the tertiary and quaternary rainbows, which are separated by only a few degrees with their colors reversed and their red arcs adjacent to each other.³

That proximity makes intuitive sense. A fourth internal reflection sends the light out at a slightly different angle from the third, so the two arcs land close together in the same part of the sky near the sun. Because the color sequences are reversed relative to each other, their red edges face one another, creating a distinctive paired appearance once the image processing strips away the glare.

A few years later, a natural fifth-order (quinary) rainbow was also photographed. This one showed up in a surprising place: not near the sun, but within Alexander’s dark band, the dim region between the primary and secondary rainbows on the antisunward side of the sky. In contrast-enhanced images, it appeared as broad green and blue-violet color bands, and its first supernumerary arc was also visible. A comparison with a numerical simulation confirmed that the color bands appeared at the expected angular location for a fifth-order bow.⁴

The fifth-order rainbow’s location between the primary and secondary bows is not a coincidence. The geometry of five internal reflections happens to send light back toward the antisunward sky at an angle that falls between the primary and secondary arcs. Each order of rainbow has its own exit angle determined entirely by the number of reflections, and those angles do not march in a tidy sequence. Some higher-order bows overlap lower-order ones, some land on the sunward side, and some end up in completely different parts of the sky.

Hundreds of Rainbows in a Single Drop

In the lab, the constraints of natural weather vanish. Researchers have observed extraordinarily high-order rainbows using controlled setups. In one experiment, a pendant water drop illuminated by a 50-milliwatt laser beam produced visible rainbows up to the 200th order.⁵ Each of these corresponds to light that has bounced 200 times inside a single drop before exiting. With a coherent laser source and a stationary drop, there is no glare from millions of other drops, no shifting wind, and no variation in drop size. The rainbow signal at each order is still progressively weaker, but with a dark background and a sensitive detector, even the faintest arcs become measurable.

These lab results are not just curiosities. They confirm that the physics of internal reflection continues to work at arbitrarily high orders. There is no fundamental cutoff where rainbows stop forming. The practical cutoff in nature is set entirely by the competing background light, the spread of raindrop sizes (which smears each arc), and the limits of human perception or camera sensitivity.

Why Raindrop Size and Shape Matter

Textbook descriptions of rainbows usually assume perfectly spherical raindrops, but real raindrops are not spheres. Small drops (under about one millimeter across) are nearly spherical because surface tension dominates. Larger drops become increasingly flattened on the bottom by aerodynamic forces as they fall, taking on an oblate shape sometimes compared to a hamburger bun. This flattening changes the angles at which light exits the drop and alters the rainbow’s appearance in ways that classical spherical theory cannot explain.

Modern rainbow theory accounts for these oblate shapes and for the fact that any real rainstorm contains a broad mix of drop sizes. Including these factors is essential for explaining observed features of natural rainbows, such as reduced color richness in bows formed by smaller drops and shifts in arc position at low sun elevations.⁶ For higher-order rainbows like the tertiary, the drop-size distribution matters even more. A wide spread of sizes blurs each order’s arc into a broader, more washed-out band, making it harder to distinguish from the background. A narrow distribution of medium-sized drops, by contrast, produces a sharper arc. This is one reason the visibility analysis of natural tertiaries found that only particular raindrop size distributions could produce a visible bow.¹

The same physics produces supernumerary bows, those faint pastel bands that sometimes appear just inside the primary rainbow. Supernumeraries arise from interference between light waves that have traveled slightly different paths through the drop, and they are most prominent when the drops are small and uniform. A broad mix of drop sizes washes them out. The fact that a supernumerary arc was detected alongside the natural fifth-order rainbow suggests that the rainstorm in question had an unusually narrow distribution of drop sizes, an atmospheric stroke of luck that amplified the signal.⁴

Twinned Rainbows and Other Oddities

The renewed interest in higher-order rainbows over the past two decades has coincided with the documentation of a range of other unusual rainbow phenomena. Twinned rainbows, where the primary bow appears to split into two separate arcs that diverge from each other, have been photographed and explained using models that account for non-spherical drop shapes and mixed drop populations.⁷ A twinned bow looks superficially like a double rainbow but is different. In a standard double rainbow, the second arc is a secondary rainbow (from a second internal reflection) with reversed colors and a wider radius. In a twinned rainbow, both arcs are primary-order bows produced simultaneously by two distinct populations of drops with different sizes or shapes, each population bending light to a slightly different angle.

Rainbows generated by nearby artificial light sources, such as streetlights illuminating a fountain, have also been documented and analyzed. Because these light sources are close to the drops rather than effectively infinitely far away like the sun, the geometry changes. The resulting arcs can be hyperbolae or other conic sections rather than circles, and the color spread differs from a solar rainbow. These are admittedly niche observations, but they illustrate how much unexplored territory remained in rainbow science even in the twenty-first century.

What It Takes to Spot a Higher-Order Rainbow Yourself

If you want to try to see or photograph a tertiary rainbow, the odds are stacked against you, but they are not zero. The conditions that give you the best chance are specific: the sun should be shining brightly and unobstructed, while a dark, rain-bearing cloud sits roughly 40 to 50 degrees from the sun as viewed from where you stand. The dark cloud provides contrast behind the arc. A rainstorm in which the drops are relatively uniform in size and medium-diameter (around one to two millimeters) will produce a sharper, more vivid arc than one with a wide mix of sizes.

For photography, shoot in RAW format to preserve the maximum dynamic range. The rainbow’s signal is buried in the bright sky, and JPEG compression discards the subtle tonal differences you need. Post-processing involves subtracting the smooth sky gradient to reveal the residual color pattern, similar to what the researchers did in the first confirmed photograph. Stacking multiple exposures can improve the signal-to-noise ratio further.

Realistically, most photographers who attempt this will not succeed on any given outing. The atmospheric conditions are rare, the signal is extraordinarily faint, and even with processing you might not be able to distinguish a genuine arc from camera noise. But the fact that several independent teams have now succeeded with consumer-grade digital cameras proves that it is within reach of dedicated amateurs. Twenty years ago, no confirmed image existed. Today, the bottleneck is patience and weather, not technology.

Alexander’s Dark Band and the Geography of Rainbow Orders

One of the more counterintuitive facts about higher-order rainbows is where they show up in the sky. The primary and secondary rainbows both appear on the antisunward side, separated by a dim region called Alexander’s dark band. That band is darker than the sky above the secondary or below the primary because no first- or second-order light is directed into that angular zone. Light that enters a drop at the angles corresponding to Alexander’s band either escapes after one reflection at too steep or too shallow an angle, or it undergoes additional reflections and exits elsewhere.

The third- and fourth-order rainbows break the pattern entirely by appearing on the sunward side, near the sun. The fifth-order arc loops back to the antisunward side and falls inside Alexander’s dark band. The sixth-order bow is predicted to sit near the secondary rainbow. Higher orders continue to alternate sides and scatter across the sky in a pattern that reflects the complex geometry of multiple internal reflections. In practice, none above the fifth order has been photographed in nature, and even the third through fifth were only revealed through image processing. The theoretical positions of these arcs have been calculated with precision, but the real sky rarely cooperates enough to display them.