A rainbow is an optical phenomenon resulting from the interaction of sunlight with atmospheric water droplets, created when light is refracted, reflected, and dispersed within these drops, forming a multicolored arc. The common perception that rainbows are always found in the east is inaccurate; their location depends entirely on the sun’s position relative to the observer. The single requirement for seeing a rainbow is that the sun must always be directly behind the person looking at it. This fixed geometric relationship dictates exactly where the colorful arc will appear in the sky.
The Geometry of Rainbow Formation
The location of a rainbow is governed by a precise geometric relationship centered on a point in the sky known as the anti-solar point. This point is defined as the location exactly opposite the sun’s position relative to the observer.
The rainbow arc is always centered on the anti-solar point. For a primary rainbow, the light is most intensely concentrated at an angle of approximately 42 degrees away from this center. Every raindrop that contributes to the rainbow you see is located along an imaginary cone with a 42-degree angle, with your eye at the tip.
The physical mechanism involves sunlight entering the droplet, bending (refracting), reflecting off the back inner surface, and then bending again as it exits toward the observer’s eye. Because each color of light bends slightly differently, they separate into the familiar spectrum.
The Time-of-Day Rule for Directional Appearance
Applying the anti-solar point rule to the sun’s daily path explains why the rainbow’s directional appearance changes. Since the sun rises in the East, the anti-solar point, which is 180 degrees away, must be located in the western sky in the morning. Therefore, any rainbow visible during a morning shower will be seen arching across the sky toward the West.
As the day progresses and the sun moves westward across the sky, the anti-solar point simultaneously moves eastward. By late afternoon or early evening, when the sun is setting in the West, the anti-solar point is positioned in the East. Consequently, rainbows observed in the evening are always found in the eastern sky.
This movement confirms that rainbows are only in the East when the sun is in the West. The directional rule is absolute: always look away from the sun to find the rainbow.
Why Rainbows are Rarely Seen at Midday
The visibility of a rainbow is also determined by the sun’s altitude, or its height above the horizon. Since the rainbow arc is fixed at about 42 degrees around the anti-solar point, the sun must be relatively low in the sky for the arc to be visible above the ground. The lower the sun, the higher and more complete the rainbow appears.
When the sun is at an elevation of 42 degrees above the horizon, the top of the primary rainbow arc is just barely touching the horizon line. If the sun rises any higher than 42 degrees, the entire rainbow arc is pushed below the horizon, making it impossible to see from ground level. At noon, the sun is often near its zenith, placing it well above the 42-degree threshold.
This is why rainbows are rarely observed at midday, even if it is raining. The anti-solar point is so far below the observer that the necessary water droplets are positioned too low to be seen against the sky. The only exception is if a person views the phenomenon from a high vantage point, such as a mountain or an airplane, allowing a full circular rainbow to be seen.