A rainbow is a full circle, not just the arc you see stretching across the sky. The reason most people never witness the complete ring is simple geometry: the ground gets in the way. The center of every rainbow sits at a point directly opposite the sun from your perspective, which means it is always below the horizon when you are standing on flat land. Raise yourself high enough or remove the ground entirely, and the rest of the circle comes into view.
Why the Ground Hides Half the Show
To understand why rainbows are circles, you need to picture how sunlight interacts with a curtain of raindrops hanging in the air in front of you. When white light enters a spherical raindrop, it slows down, bends (refracts), bounces off the back wall of the drop, and bends again on its way out. That process sends light back toward you at a very specific angle: roughly 42 degrees from the line connecting the sun, your head, and a point on the ground called the antisolar point. That antisolar point is where your shadow’s head would be if you could see it projected far into the distance.
Every raindrop that happens to sit at exactly 42 degrees from that line sends colored light to your eyes. And the collection of all possible directions that are 42 degrees away from a central axis forms a cone. Slice a cone with a flat surface and you get a circle. So the rainbow you see is the visible portion of a cone of light, and it is inherently circular. When you stand on the ground, the lower half of that circle falls below the horizon, leaving only the familiar arc. The lower the sun sits in the sky, the higher the antisolar point rises behind you (though it always stays below the horizon), and the more of the circle peeks above the ground. That is why late-afternoon and early-morning rainbows are taller and more dramatic than midday ones, when the sun is high and the arc barely clears the landscape.
Seeing the Full Circle
Pilots and passengers in aircraft sometimes look down and spot a complete circular rainbow projected onto a cloud layer or mist below. The same thing happens at tall waterfalls: if you are positioned above the spray and the sun is behind you, a full 360-degree ring of color can appear in the mist. You can even create one in your backyard with a garden hose on a sunny day. Stand with the sun at your back, spray a fine mist, and look for the arc. If the spray extends far enough below your eye level, the bottom of the circle fills in. These miniature rainbows are the easiest way to confirm for yourself that the arc really is just a fragment of a ring.
Mountaineers and skydivers report seeing similar full-circle bows, sometimes accompanied by a glory, which is a separate optical effect that appears as small concentric colored rings around the shadow of your head on a cloud. The two phenomena arise from different physics but share the requirement that you be elevated above a layer of water droplets.
Why Exactly 42 Degrees
The specific angle is not arbitrary. It comes from the way light refracts when it crosses from air into water and back. Red light bends slightly less than violet light, so the outer edge of the rainbow (at about 42 degrees) is red and the inner edge (about 40 degrees) is violet, with the rest of the spectrum arranged between them. This spread of angles is what gives the rainbow its width of roughly two degrees.
The 42-degree figure applies specifically to the primary rainbow, which involves one internal reflection inside the raindrop. Because the physics locks each color to a narrow range of exit angles, light concentrates near these values instead of scattering evenly in all directions. That concentration is why a rainbow appears as a bright, defined band rather than a vague wash of color across the sky.
The Secondary Rainbow and the Dark Band Between Them
If you look carefully during a strong rain shower, you can often spot a second, fainter rainbow outside the primary one. This secondary bow forms when light bounces twice inside each raindrop before exiting. The extra reflection reverses the color order: red is on the inside and violet is on the outside, the opposite of the primary bow. It also appears at a wider angle, roughly 51 degrees from the antisolar point, so it arcs above the primary rainbow.
The strip of sky between the primary and secondary rainbows looks noticeably darker than the sky on either side. This region is called Alexander’s dark band, named after Alexander of Aphrodisias, who described it in the third century. The darkness occurs because light that enters raindrops in that angular range does not get directed back to your eyes efficiently; it falls between the concentration angles of the two bows. Research on non-spherical drops has shown that when raindrops are slightly flattened by air resistance (an aspect ratio near 1.08), additional faint ray paths can push some light into parts of Alexander’s dark band, but under normal conditions the band remains visibly dim.
Higher-Order Rainbows
Beyond the primary and secondary bows, light can bounce three, four, five, or even more times inside a raindrop, each time producing a higher-order rainbow. These bows are progressively fainter because each internal reflection loses some light, and their positions shift in ways that make them extremely hard to see. The tertiary (third-order) rainbow, for instance, appears on the same side of the sky as the sun rather than opposite it, which means it is largely drowned out by direct sunlight and forward-scattered glare. For a long time, sightings of the tertiary bow were limited to a handful of unconfirmed visual reports. The first reliable photographic evidence for a naturally occurring third-order rainbow was eventually obtained, confirming its existence after decades of theoretical prediction and attempted observation.1PubMed Central. Photographic evidence for the third-order rainbow
Fourth- and fifth-order rainbows also appear near the sun’s position, making them even harder to detect against the bright sky. In controlled laboratory settings using laser light and single suspended droplets, researchers have observed these higher-order bows clearly, confirming that the physics works exactly as predicted. In nature, spotting anything beyond the secondary rainbow without specialized imaging techniques or contrast-enhancing filters remains a rare feat.
Supernumerary Arcs
If you look at the inner edge of a vivid primary rainbow, you may notice faint pastel bands of pink and green repeating inward. These are supernumerary arcs, and they cannot be explained by the simple ray-tracing picture of light bouncing inside a raindrop. They arise because light is a wave, and two wave paths that exit a raindrop at nearly the same angle can interfere with each other, reinforcing at some angles and canceling at others. Thomas Young proposed this interference explanation in the early 1800s, recognizing that two rays emerging from the drop at the same scattering angle could produce the alternating bright and dark fringes.2PubMed. Supernumerary arcs of rainbows: Young’s theory of interference
The spacing of supernumerary arcs depends on the size of the raindrops. Smaller drops produce wider spacing, while larger drops push the fringes closer together. In a natural rain shower where drops come in many sizes, the supernumerary fringes from different drop sizes overlap and blur each other out, which is why you typically only see them when the rain is composed of unusually uniform small droplets. This same sensitivity to drop size makes supernumerary arcs a useful natural indicator: their spacing tells atmospheric scientists something about the droplet population producing the bow.
Fogbows and White Rainbows
When the water droplets responsible for the bow are very small, as in fog or thin mist, the resulting arc loses most of its color and appears as a ghostly white or faintly tinted band. This is a fogbow. The physics is the same as an ordinary rainbow, but because the droplets are tiny (often well under a tenth of a millimeter), the wave-interference effects spread the colors so broadly that they overlap and wash out into white.
Fogbows vary quite a bit in appearance depending on the fog itself. Measurements of fogbows in the high Arctic revealed substantial variation in both the width of the bow and the spacing of any accompanying supernumerary fringes, even along different parts of the same fogbow. Some fogbows were relatively uniform in appearance, while others showed dramatic changes from one side to the other, reflecting the spatially uneven droplet sizes produced by patchy conditions over open water and ice.3PubMed Central. Imaging polarimetry of the fogbow: polarization characteristics of white rainbows measured in the high Arctic
Because fogbows are broader and dimmer than rainbows, they are easy to miss unless you know what to look for. The best conditions are a thin fog bank with the sun low and behind you, the same geometric setup as a normal rainbow. Sailors, mountaineers, and polar researchers encounter them most often.
Rainbows Are Polarized
One property of rainbows that is invisible to the naked eye but detectable with polarizing sunglasses is that the light in a rainbow is strongly polarized. The refraction and reflection inside a water droplet preferentially transmit light vibrating in one plane, particularly near the rainbow angle. If you rotate a pair of polarized sunglasses while looking at a rainbow, you will see the bow brighten and dim as you change the orientation, a simple demonstration of this effect.
Theoretical work extending the standard Airy description of rainbows to account for polarization has shown that the degree of polarization is somewhat less than the simplest geometric prediction would suggest, and that it depends on the size of the raindrops: larger drops produce more strongly polarized light.4Optica Publishing Group (Applied Optics). Polarized rainbow This polarization is not just a curiosity. It helps researchers studying fogbows and other faint atmospheric optics phenomena isolate the bow’s signal from the surrounding skylight, and it occasionally matters for photographers who use polarizing filters and find that a rainbow vanishes or intensifies unexpectedly depending on the filter’s angle.
Every Person Sees a Different Rainbow
A subtle consequence of the rainbow’s geometry is that no two people ever see exactly the same one. Because the rainbow is defined by the angle between the sunlight, the water droplets, and your eyes, your rainbow is centered on your antisolar point, and your antisolar point depends on where your eyes are. A person standing ten feet to your left has a slightly different antisolar point and is receiving light from a slightly different set of raindrops. You are both seeing a rainbow, but not the same physical collection of light. Move your head and the rainbow moves with you, always maintaining that 42-degree cone.
This is also why you can never walk to the “end” of a rainbow or find the proverbial pot of gold. The bow is not located at any fixed point in space; it exists only as a directional relationship between the sun, the drops, and your eyes. As you walk toward it, the drops producing the light you see shift further away, and the rainbow retreats at the same pace. The same logic applies to the full circle: it is not a ring floating in space at a fixed altitude. It is a cone of angles centered on your personal line of sight, projected onto whatever droplets happen to be in the right positions.
Halos, Glories, and Other Rings in the Sky
Rainbows are not the only circular optical phenomena in the atmosphere, and casual observers sometimes confuse them with related effects. A halo, typically seen as a ring around the sun or moon, is produced by ice crystals in high-altitude cirrus clouds rather than by water droplets. The most common halo appears at 22 degrees from the sun, a distinctly different angle and mechanism from a rainbow’s 42-degree geometry.5CrossRef API (Optica Publishing Group). Observations of Halo Scattering From Single Ice Crystals Halos tend to look whitish or faintly iridescent, and they encircle the sun itself rather than appearing opposite it.
Glories, mentioned earlier, are the small concentric colored rings you sometimes see around the shadow of an airplane on a cloud below. They are caused by backscattering and wave effects in very small water droplets, not by the refraction-and-reflection process that produces rainbows. Coronas, the colored rings sometimes visible directly around the sun or moon when thin clouds pass in front of them, are yet another distinct phenomenon caused by diffraction around cloud droplets. All of these are circular, all involve light interacting with water or ice in the atmosphere, but each one relies on a different physical mechanism and appears at a different position relative to the sun and observer.
Why Drop Shape Matters
The classic explanation of rainbows assumes perfectly spherical droplets, and small raindrops (under about two millimeters in diameter) are close enough to spherical that the idealized picture works well. Larger drops, though, get squashed by air resistance into a slightly flattened shape, like a hamburger bun. This distortion changes the angles at which light exits and subtly alters the rainbow’s appearance. A rainbow produced by large, oblate drops can appear slightly flattened at the top, brighter along the sides, or show unusual color distributions.
Laboratory experiments using suspended drops with controlled aspect ratios have demonstrated how even modest flattening alters the fine structure of the rainbow, producing additional ray paths and modifying the cusps and folds in the light pattern.6PubMed Central. Generalized rainbows and unfolded glories of oblate drops: organization for multiple internal reflections and extension of cusps into Alexander’s dark band In practice, natural rain showers contain drops of many sizes, so these deviations from the idealized round-drop rainbow tend to average out. But during showers dominated by large drops, keen observers have noticed that the top of the rainbow can appear slightly compressed or that colors shift in unexpected ways. These observations match the predictions of models that account for drop deformation, and they add one more layer to why real rainbows always look a bit different from the textbook diagrams.