The rainbow is a vibrant optical display, but how rare it is depends entirely on what is meant by “full.” The familiar semi-circular arc is a frequent occurrence under the right meteorological circumstances. However, the phenomenon is geometrically a complete circle. Seeing this true, 360-degree form is exceptionally uncommon for an observer on the ground. The difference between the common arc and the rare full circle is determined by scientific geometry and the observer’s specific vantage point.
The Geometry of a Rainbow
Every rainbow a person sees is fundamentally a circular phenomenon, even if only a segment is visible. This fixed shape is determined by the precise physics of how sunlight interacts with spherical water droplets. When a ray of white sunlight enters a raindrop, it refracts, separating into its constituent colors, then reflects off the back inner surface of the droplet, and finally refracts again as it exits toward the viewer’s eye.
The most intense light returns to the observer at a fixed angle of approximately 42 degrees from the path of the incoming sunlight. This specific angle, known as the rainbow angle, is constant for all observers and all primary rainbows, regardless of the size of the water droplets. Because this 42-degree condition is met in all directions around a central axis, the resulting light pattern is always a perfect circle.
The center of this circle is the antisolar point, the spot directly opposite the sun from the viewer’s perspective. This point is always located precisely at the shadow of the observer’s head. Since the geometry is defined by the viewer’s position relative to the sun and the raindrops, every person sees a slightly different, personal rainbow centered on their own shadow.
Why We Rarely See the Complete Circle
The rarity of a “full rainbow” is directly tied to the viewing environment, as the atmosphere is constantly forming the complete 360-degree circle. The primary reason a person on the ground only sees a semi-circular arc is because the horizon physically obstructs the lower half of the circle. The ground prevents the necessary water droplets in the lower atmosphere from being illuminated at the correct 42-degree angle relative to the observer.
To view the full, truly circular rainbow, an observer must be elevated high enough so that the horizon does not interfere with the geometry. This specific condition is met most reliably from an aircraft, where the observer is positioned high above the cloud layer containing the raindrops. The full circle can also be seen from the top of a very tall mountain or a high-rise building with a rain shower below.
Seeing the full circle on the ground is highly improbable, but partial views are sometimes achieved over large bodies of water. In these cases, the horizon may be low enough and the mist high enough to reveal slightly more than the typical 180-degree arc.
Conditions for Maximum Rainbow Visibility
The clarity and brightness of any rainbow, whether a full circle or a partial arc, depends on a few specific atmospheric conditions. The sun’s position is one of the most important factors, as the sun must be low in the sky, ideally less than 42 degrees above the horizon. This is why rainbows are most often seen in the late afternoon or early morning, as a sun higher than 42 degrees places the entire rainbow circle below the horizon.
The size of the water droplets within the rain shower also significantly influences the display’s quality. Larger raindrops, typically those over a millimeter in diameter, produce a brighter and more vivid rainbow with clearly separated colors. Smaller droplets, such as those found in fog or mist, cause the colors to overlap more, resulting in a paler, broader, and sometimes nearly white phenomenon known as a fogbow.
Atmospheric clarity is another factor, as low levels of haze, dust, or pollution allow sunlight to reach the raindrops with maximum intensity. For the most spectacular displays, the sun should be shining brightly behind the observer while the opposite sky, where the rainbow forms, is dark with rain clouds. This contrast allows the colors to stand out vividly against the darkened background.