A rainbow is an optical phenomenon that occurs when sunlight interacts with tiny water droplets suspended in the air. The familiar arc shape seen from the ground results from light being refracted and internally reflected inside these spherical drops. Although we typically perceive a rainbow as a semicircle, its formation dictates that the shape is fundamentally a full, 360-degree circle.
The Fixed Geometry That Creates a Circle
The circular nature of the rainbow is governed by a precise angle of light deviation. When a ray of sunlight enters a spherical raindrop, it first bends, or refracts, then reflects off the back inner surface of the drop, and finally refracts again upon exiting. This three-step process separates the white sunlight into its component colors, a process known as dispersion.
The most intense light for the primary rainbow returns to the observer at a consistent angle of approximately 42 degrees relative to the path of the incoming sunlight. This specific angle is the result of geometric and optical principles that concentrate the light rays. Red light, which is refracted the least, appears at the outermost edge of the bow at about 42 degrees, while violet light is seen near the inner edge at roughly 40 degrees.
For an observer, every water droplet that is positioned at this specific 40-to-42-degree angle away from the line connecting the observer’s eye and the sun will contribute to the rainbow. Because this angle is constant in all directions around that central line, the collection of illuminated droplets forms a cone of light with the observer’s eye at the apex. The visible base of this cone is what creates the perfect circular shape of the rainbow.
The Role of the Horizon in Obscuring the View
A full circle rainbow is rarely seen from the ground due to the obstruction of the horizon. The center of any rainbow is always a point in the sky directly opposite the sun, known as the anti-solar point. This point lies on a line that runs from the sun, through the observer, and continues behind them.
When the sun is low on the horizon, the anti-solar point is located on the opposite horizon, allowing the observer to see a full semicircle above the ground. As the sun rises higher in the sky, the anti-solar point sinks lower toward the ground, causing the rainbow arc to appear smaller and lower. The Earth’s surface effectively cuts off the bottom half of the circle.
A partial rainbow is only possible when the sun’s altitude is less than 42 degrees above the horizon. Once the sun rises past this 42-degree threshold, the anti-solar point drops more than 42 degrees below the horizon. At this point, the entire potential rainbow circle is pushed below the observer’s horizon and becomes completely invisible from ground level.
Ideal Conditions for Observing the Complete Circle
To overcome the obstruction of the ground, an observer needs to be elevated above the horizon with water droplets present below them. The most common location to witness a full, 360-degree circular rainbow is from an aircraft flying above a cloud or rain layer. From this vantage point, the observer is high enough to see the lower portion of the bow that would otherwise be blocked by the ground.
A similar opportunity can arise when viewing the phenomenon from very high mountains or tall observation decks, provided there is mist or rain in the air at a lower elevation. In these cases, the observer looks down upon the entire cone of light being reflected by the droplets. The center of the circle remains the anti-solar point, which is often visible as the shadow of the observer or the aircraft.
While a natural full-circle rainbow requires specific high-altitude viewing, a complete bow can also be created artificially on the ground. This is done by spraying a fine mist of water from a garden hose while standing with the sun directly behind the observer. This method creates a small, personal full-circle rainbow because the water droplets are close enough that the lower part of the bow is not blocked by the distant horizon.