A rainbow is one of nature’s most recognizable optical phenomena, appearing as a colored arc in the sky. This visual spectacle is created when sunlight interacts with suspended water droplets in the atmosphere, combining the processes of refraction, reflection, and dispersion. The common view of a rainbow is a semi-circle resting on the horizon, leading most people to assume its shape is simply an arc. The visual evidence from the ground, however, is a deceptive trick of perspective that obscures the true, three-dimensional geometry of the phenomenon. In reality, the physical structure of a rainbow is a complete, unbroken circle.
The Geometry of the 42-Degree Cone
The circular shape of the rainbow is an effect governed by precise optics occurring within each water droplet. When a ray of sunlight enters a spherical raindrop, it first refracts, or bends, and simultaneously separates into its constituent colors. The light then reflects off the back interior surface of the droplet, and finally refracts again as it exits and travels back toward the observer. This specific sequence of events creates a maximum concentration of light intensity at a particular angle.
This maximum angle of deviation for the returning light is approximately 42 degrees from the path of the incoming sunlight. Because the angle is fixed, all the raindrops that reflect light back to the observer’s eye at this specific angle form a cone shape. The observer’s eye is situated at the apex of this cone, and the rainbow itself is the visible, circular base of the light cone.
The specific angle of light return differs slightly for each color due to dispersion. Red light emerges at the largest angle (around 42.5 degrees), forming the outermost band. Violet light emerges at a smaller angle (approximately 40.6 degrees), creating the innermost band. The center of this circular structure is the anti-solar point, the spot in the sky directly opposite the sun.
Why the Horizon Limits the View
We typically see only an arc because the ground obstructs the view. The complete circular rainbow centers on the anti-solar point, which is always located below the horizon whenever the sun is visible. The Earth’s surface cuts off the bottom portion of the full circle, leaving only the upper segment visible.
The size of the visible arc depends on the sun’s altitude. As the sun rises higher in the sky, the anti-solar point drops lower, and a smaller portion of the circular rainbow remains above the horizon. If the sun climbs higher than 42 degrees above the horizon, the entire 42-degree circle drops below the horizon, and no rainbow can be seen. This explains why rainbows are most often sighted during the late afternoon or early morning, when the sun is low.
Observing the Complete Circular Rainbow
The full circular shape can be observed whenever the ground obstruction is removed. This is most commonly achieved by viewing the phenomenon from an aircraft flying at a high altitude. From this elevated vantage point, the observer is surrounded by water droplets extending below the normal horizon, allowing the entire light cone to be seen.
A complete circular rainbow can also be viewed from the top of a tall mountain or tower. The necessary conditions are met in any environment where the observer is positioned high above a dense cloud of airborne water droplets or mist. When the full circle is seen in localized spray, such as near a powerful waterfall or a high-pressure garden hose, the phenomenon is often referred to as a “glory” or a circular bow.