A rainbow is a captivating natural spectacle, frequently gracing the sky after rain. It consistently appears as a vibrant, multi-colored arc. Its distinct curved shape results from specific interactions between sunlight and countless water droplets. Understanding the science behind this consistent arc reveals fundamental principles of light and optics.
Light’s Journey Through Raindrops
Rainbow formation begins with sunlight encountering individual water droplets. As white sunlight enters a raindrop, it undergoes refraction, bending the light. This bending occurs because light changes speed as it passes from one medium (air) to another (water), slowing down and altering its path. This initial bending helps separate the sun’s white light.
After entering the raindrop, the light travels to the opposite side of the droplet. Here, it experiences internal reflection, bouncing off the back inner surface of the raindrop and redirecting the light back towards the front. This reflection sends the light back towards the observer. As the light exits the raindrop and re-enters the air, it undergoes a second refraction, bending once more.
This sequence of two refractions and one internal reflection separates white light into its constituent colors, a process known as dispersion. Different colors, or wavelengths, of light bend at slightly different angles during refraction. Red light, with its longer wavelength, bends the least, while violet light, with its shorter wavelength, bends the most, effectively fanning out the spectrum. This differential bending ensures the distinct bands of color observed in a rainbow.
The Angular Geometry of the Arc
The curved shape of a rainbow arises from the angles at which light emerges from millions of raindrops. Due to refraction and internal reflection, sunlight exits a raindrop at a consistent angle relative to the incoming sunlight. For red light, this angle is approximately 42 degrees, and for violet light, it is slightly less, around 40 to 40.7 degrees. Other colors emerge at angles between these two extremes.
Observers see light from raindrops positioned at specific angles relative to their eye and the sun. These raindrops form a cone of light, with the observer’s eye at the apex and the sun’s rays forming the axis. The cone’s center aligns with the anti-solar point, directly opposite the sun.
Only raindrops along this cone’s surface send colored light directly to the observer’s eye, creating a circular arc. Millions of individual raindrops contribute a single color to the overall spectrum seen by the observer. Each individual sees their own unique rainbow, determined by their location relative to the sun and rain.
Why We See an Arc and Not a Full Circle
A rainbow is geometrically a full circle, but for ground observers, the horizon typically blocks the lower portion. This obstruction prevents light from raindrops below the horizon from reaching the eye, making it appear as a semi-circular arc. The amount visible depends on the sun’s elevation; a lower sun allows more of the rainbow arc to become visible above the ground.
A full circular rainbow can be observed from an elevated vantage point, such as an airplane or tall building. From such heights, the horizon no longer obstructs the view, allowing the entire 360-degree phenomenon to be seen. The anti-solar point, directly opposite the sun, serves as the center of this complete rainbow circle. This point aligns with where an observer’s shadow would fall if projected onto the rain.
This clarifies that the arc we commonly see is a segment of a larger, inherent circular shape. The perception of an arc is a consequence of the observer’s ground position relative to the rainbow’s geometric center. Each person’s unique position dictates which part of this universal circular phenomenon they perceive.