Rainbows are captivating displays of light and color that emerge in the sky, often after a rain shower. While a single, vibrant arc is a common sight, occasionally a second, fainter bow appears outside the primary one, creating a double rainbow. The secondary arc’s color sequence is inverted compared to the main rainbow. This phenomenon, though seemingly complex, arises from specific interactions between sunlight and water droplets in the atmosphere.
How a Single Rainbow Forms
A primary rainbow forms when sunlight interacts with water droplets suspended in the air. As white sunlight enters a spherical raindrop, it bends, called refraction, and separates into its constituent colors, much like light passing through a prism. Each color of light bends at a slightly different angle due to its unique wavelength. Red light bends the least, while violet light bends the most.
After entering the droplet and dispersing, the light travels to the back inner surface of the droplet. There, it undergoes a single internal reflection. The light then travels back through the droplet and refracts once more as it exits the droplet. This combined process of two refractions and one internal reflection causes the familiar arc with red on the outside and violet on the inside.
The Second Reflection
The formation of a secondary rainbow involves an additional reflection within water droplets. Instead of just one internal reflection, the light undergoes two internal reflections inside the raindrop. This means that after the initial refraction upon entering the droplet, the light reflects off the back surface, then travels across the droplet to reflect off another point on the inner surface.
This second reflection alters the light path, causing it to exit at a different angle than the primary rainbow. The secondary bow appears about 10 degrees outside the primary bow and is typically fainter because some light is lost with each reflection. This additional reflection creates a second, wider arc of color in the sky.
The Inversion Explained
The inverted color sequence in a double rainbow results from this second internal reflection. In the primary rainbow, red light exits at approximately a 42-degree angle relative to the incoming sunlight, while violet light exits at about 40 degrees, placing red on the outer edge. For the secondary rainbow, the light path is flipped due to the extra bounce.
The light that produces the secondary rainbow emerges from the raindrop after reflecting twice, causing it to exit at a different angular range, approximately between 50 and 53 degrees. This additional reflection causes the light rays to cross over inside the droplet, reversing the order of the colors. Consequently, the secondary rainbow displays violet on its outer edge and red on its inner edge, making it an inverted version of the primary bow.
Alexander’s Dark Band
Between the primary and secondary rainbows, a darker strip of sky appears, known as Alexander’s Dark Band. This phenomenon is named after Alexander of Aphrodisias, who described it around 200 AD. The dark band is an area where very little sunlight is scattered by raindrops towards the observer.
Light rays that form the primary rainbow brighten the sky inside its arc, while rays forming the secondary rainbow brighten the sky outside its arc. However, specific reflection and refraction angles mean no light is directed from droplets in the region between the two bows. This absence of scattered light creates the distinct dark band.