A rainbow is an optical event that occurs when sunlight interacts with water droplets suspended in the atmosphere. Sunlight interacts with water droplets, bending and splitting light to create a visible spectrum of colors. While a single, vibrant arc is a common sight, a double rainbow presents a more complex and equally captivating display, often prompting questions about its unique formation.
How a Single Rainbow Forms
Primary rainbows form when sunlight enters raindrops. As light enters the denser water, it refracts, bending and slowing down. This bending separates white sunlight into its constituent colors, like a prism, because each color bends at a different angle. Blue and violet light, having shorter wavelengths, bend more than red light.
Once inside the raindrop, the separated light rays travel to the opposite inner surface of the drop. Here, they reflect once off the back of the droplet, similar to how light reflects off a mirror. After this single internal reflection, the light travels back towards the front of the raindrop.
The light undergoes a second refraction as it exits the raindrop and re-enters the air. This further separates the colors and directs them towards an observer, creating the familiar arc. For a primary rainbow, red light emerges at an angle of approximately 42 degrees relative to the incoming sunlight, while violet light exits at about 40 degrees, placing red on the outside and violet on the inside of the bow.
Unpacking the Double Rainbow Phenomenon
A double rainbow, or secondary bow, forms from a more intricate interaction of sunlight within raindrops. It is not simply a direct reflection of the primary rainbow. Instead, the secondary bow forms due to light reflecting twice inside the raindrop.
This additional internal reflection causes the light to exit the raindrop at a different angle compared to the primary rainbow. While the primary bow forms at angles between 40 and 42 degrees from the antisolar point (the point directly opposite the sun), the secondary bow appears further out, between 50 and 53 degrees. This larger angle places the secondary rainbow outside and above the primary one.
The extra reflection inside the raindrop also accounts for the secondary bow’s fainter appearance and its inverted color order. Each reflection causes some light to be lost, so light that undergoes two reflections emerges with less intensity. The second reflection reverses the color order, leading to the distinctive sequence.
Distinguishing Features of Double Rainbows
Several features differentiate the primary and secondary bows. A key difference is the color order. In the primary rainbow, red appears on the outer edge and violet on the inner edge. Conversely, the secondary rainbow exhibits an inverted color sequence, with red on the inside and violet on the outside.
The secondary rainbow is fainter and wider than the primary bow. This reduced brightness is a direct consequence of the extra internal reflection, as more light is dispersed and lost during the extra internal reflection. The increased width is due to the light being spread over a greater angular extent.
Alexander’s Dark Band is a darker region of sky between the primary and secondary rainbows. This band appears dark because raindrops in this area do not direct light towards the observer. Light rays either contribute to the primary bow by reflecting once or to the secondary bow by reflecting twice, leaving the space between them devoid of direct light.