Rainbows, with their vibrant spectrum of colors arcing across the sky, are a captivating sight. Their beauty and temporary nature have long fascinated observers. The curved shape of a rainbow results from a precise interplay of light and water, revealing the physics behind this spectacular display.
Light’s Journey Through Water
The formation of a rainbow begins with sunlight interacting with individual water droplets suspended in the atmosphere. When white light from the sun enters a spherical raindrop, it undergoes refraction, the bending of light as it passes from one medium to another. This bending occurs because light changes speed as it moves into the denser water, similar to how light behaves when passing through a prism.
As light refracts upon entering the water droplet, it simultaneously disperses. Different wavelengths, corresponding to different colors, bend at slightly different angles; violet light bends more than red light, for instance. This dispersion splits the white sunlight into the familiar spectrum of red, orange, yellow, green, blue, indigo, and violet within the droplet.
After entering and dispersing, the colored light travels to the back inner surface of the water droplet. Here, it undergoes internal reflection, which redirects the light back towards the observer. Finally, as the light exits the water droplet, it refracts once more, sending the colors out into the air at specific angles.
The Curved Perspective
The reason a rainbow appears curved lies in the specific angle at which light is reflected from countless water droplets back to an observer’s eye. For the primary rainbow, the most intense light returns to the observer at an angle of approximately 40 to 42 degrees relative to the anti-solar point, the point directly opposite the sun. Red light emerges at about 42 degrees, while violet light exits at roughly 40 degrees.
All the water droplets that reflect light at this precise angle to the observer form a cone shape, with the observer’s eye positioned at the apex of this cone. The axis of this cone extends from the sun, through the observer’s eye, and down to the anti-solar point. Each droplet contributing to the rainbow’s appearance is located on the surface of this imaginary cone.
When this cone of light intersects with the ground or the horizon, it creates the appearance of a circular arc. From an elevated position, a full circular rainbow can sometimes be seen because the ground does not obstruct the lower part of the circle. Each person sees a unique rainbow, as its appearance depends on their specific position relative to the water droplets and the sun. The rainbow is not a fixed object in the sky but rather an optical phenomenon created by the interaction of light, water, and the observer’s eye.