Supernumeracy Rainbows

Last updated on September 16, 2023

Supernumerary Rainbows: A Fascinating Phenomenon in Atmospheric Optics

Rainbows have captivated human imagination for centuries with their vibrant colors and ethereal beauty. Most of us are familiar with the primary rainbow, which forms when sunlight is refracted, reflected, and dispersed within raindrops. However, there is another captivating phenomenon that occurs alongside the primary rainbow - the supernumerary rainbow. These elusive fringes of color add an extra layer of intrigue to the already mesmerizing display of atmospheric optics.

What are Supernumerary Bows?

Supernumerary bows are delicate, closely spaced arcs of predominantly green, pink, and purple hues that appear just inside the primary rainbow. Unlike the primary rainbow, which has a fixed number of colors, the supernumeraries can vary in number and spacing from minute to minute. They are most commonly observed near the top of the primary bow.

The Limitations of Geometric Optics

The existence of supernumerary bows challenges the explanations provided by geometric optics alone. Geometric optics, which describes the behavior of light as rays, fails to fully account for the complex wave nature of light. To understand the formation of supernumeraries, we must delve into the wave properties of light.

The Wave Nature of Light

To comprehend the phenomenon of supernumerary bows, we need to consider the wave nature of light. When sunlight passes through raindrops, it not only undergoes refraction and reflection but also experiences interference. Interference occurs when two or more light waves overlap and either reinforce or cancel each other out.

Interference and Supernumeraries

The closely spaced supernumeraries result from the interference between light waves as they pass through raindrops. The interference pattern depends on the size and distribution of the raindrops. In the case of supernumeraries, they are created by small raindrops that have almost identical sizes.

The Role of Small Raindrops

Supernumeraries are particularly associated with small raindrops. These raindrops have a narrow size distribution, with minimal variation in their diameters. It is the consistent size of these raindrops that allows for constructive and destructive interference, leading to the formation of the supernumerary bows.

Capturing Supernumerary Bows

Photographing supernumerary bows can be a challenging task due to their subtle appearance and rapid changes. To capture these elusive fringes of color, one must be patient and observant. After a heavy shower, when raindrops are abundant, the chances of witnessing and photographing supernumeraries increase.

The Beauty of Changing Numbers and Spacing

One of the remarkable aspects of supernumeraries is their ever-changing numbers and spacing. Minute by minute, the arrangement of these colorful arcs can shift, creating a dynamic and mesmerizing display. This variability adds an element of unpredictability to the already captivating world of atmospheric optics.

Studying Supernumeraries: Simulations and Observations

Scientists have utilized simulations and observations to better understand the formation of supernumerary bows. Through computer simulations like AirySim, researchers can calculate and visualize the patterns created by raindrops of specific sizes. By comparing these simulations with real-life observations, scientists can validate and refine their understanding of this fascinating phenomenon.

Expanding Our Knowledge of Atmospheric Optics

The study of supernumerary bows expands our knowledge of atmospheric optics and reminds us of the intricate interplay between light and water droplets in the atmosphere. As we delve deeper into the wave properties of light and explore the behavior of raindrops, we uncover new layers of complexity within the realm of optical phenomena.

In conclusion, supernumerary bows are captivating additions to the primary rainbow, showcasing the wave nature of light and the delicate dance of interference within raindrops. Their ever-changing numbers and spacing provide a source of wonder and fascination, challenging our understanding of geometric optics. By studying and appreciating these ethereal fringes of color, we continue to unravel the mysteries of atmospheric optics and deepen our appreciation for the beauty and complexity of the natural world.

Multiple supernumerary bows. The supernumeraries are the closely spaced greenish purple arcs on the inner (blue) side of the primary bow. Captured by Mark Nankman at Hedeviken in Sweden after a heavy shower, August '99. ©Mark Nankman, shown with permission.

Supernumeraries are created by small, almost same sized raindrops. The diagonal inset on this contrast enhanced view is an AirySim simulation calculated for drops of 0.7mm mean dia. with only an 8% (std. dev.) spread in diameters.

Look slightly inside a bright primary bow and sometimes you will see one or more predominantly green, pink and purple fringes. Their numbers and spacing can change from minute to minute. They are seen most often near the top of the bow - example here.

These "supernumerary bows" are an intimation of the limitations of geometric optics for it is totally unable to explain them. To do so we must take account of the wave nature of light.

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