Secondary Rainbow

The Secondary Rainbow: Exploring the Phenomenon in Detail

Have you ever marveled at the beauty of a rainbow and wondered about its intricacies? While most of us are familiar with the primary rainbow, characterized by its vibrant display of colors, there is another phenomenon known as the secondary rainbow that adds an extra layer of fascination to the optical spectacle. In this article, we will delve into the details of the secondary rainbow, shedding light on its formation, unique characteristics, and the science behind its captivating appearance.

Understanding Secondary Bow Rays

The secondary bow is formed by two internal reflections within raindrops, resulting in rays that are deviated more than 180 degrees. Unlike the primary bow, which has a radius of approximately 42 degrees, the secondary bow has a larger radius of 51 degrees. This increase in radius is attributed to the minimum deviation angle of about 231 degrees, at which the secondary bow occurs.

The Journey of Light in the Secondary Rainbow

To comprehend the formation of the secondary rainbow, we must first understand the path taken by light within raindrops. When light enters a raindrop, it undergoes multiple internal reflections before exiting. In the case of the secondary rainbow, light is reflected more than twice within the raindrop. As a result, these rays enter higher order bows while forming the secondary bow.

Exploring Ray Paths and Brightness

The behavior of light rays within raindrops is a fascinating subject. Rays that contribute to the secondary bow are deviated through more than 180 degrees and cluster around the minimum deviation condition. This clustering creates the brightest part of the secondary rainbow. It is important to note that the minimum deviation rays enter much closer to the edge of the raindrop compared to those contributing to the primary bow.

The Mystery of Color Reversal

One intriguing aspect of the secondary rainbow is the reversal of colors when compared to the primary rainbow. The reason for this reversal lies in the varying degrees of refraction experienced by different colors of light. Red light, being refracted the least, suffers the smallest deviation. However, since the total deviation of the secondary bow is more than 180 degrees, the least deviated rays appear on the inside of the bow, resulting in a reversal of colors.

Unveiling Alexander's Dark Band

Between the primary and secondary bows lies a region known as Alexander's dark band. This dark band occurs because no light from the secondary rays appears at less than 51 degrees from the center, while no light from the primary rays appears beyond 42 degrees. As a result, the sky between these two angles appears relatively dark, creating a striking contrast within the rainbow.

Beyond Ray Paths: Accounting for Wave Nature

While ray paths provide a good approximation of how light behaves within raindrops of several millimeters across, it is important to consider the wave nature of light when dealing with smaller droplets. The behavior of light in such scenarios requires a more comprehensive treatment that incorporates wave properties.


The secondary rainbow is a captivating optical phenomenon that adds depth and complexity to the already mesmerizing display of colors in the sky. By understanding its formation, the journey of light within raindrops, and the intricacies of color reversal, we can appreciate the beauty of this natural spectacle even more. So, the next time you spot a rainbow, take a moment to observe both the primary and secondary bows, and marvel at the wonders of atmospheric optics.

Secondary bow rays.

There are two internal reflections and rays are deviated more than 180º. The 51° radius bow occurs at the minimum deviation angle of 231°

Light emerging after two internal reflections forms the secondary bow. Light reflected more than twice goes into higher order bows. Two internal reflections. Mouse over the slider to see the ray paths. Compare them with those of the primary bow, shown faintly here and more completely in the primary ray diagram. Many different ray paths Secondary bow rays* are deviated** through more than 180º. There is a minimum deviation of about 231º corresponding to the inner edge of the secondary bow. Its radius is therefore 231 - 180 = 51º. Rays cluster around the minimum deviation condition to form the brightest part of the bow. Minimum deviation angleThe minimum deviation rays enter much closer to the drop's edge than the corresponding rays of the primary bow. Closer to the drop edgeWhy are the secondary colours reversed? Red light is refracted least and so its rays suffer the smallest deviation. But the total deviation is more than 180º and the least deviated rays appear at the inside of the bow. Colour reversal No light from secondary rays appears at less than 51º from the center and no light from the primary appears more than than 42º. The sky between is dark (but not quite, see the 5th order bow). This is Alexanders dark band. Inside the bow is dark * Ray paths are a good approximation to how light behaves when the raindrops are several millimetres across. Smaller drops require a treatment which takes account of the wave nature of light. Don't take ray paths too seriously ** Deviations are traditionally measured from the direction of the incoming sunlight. Deviation angles *** The ray paths are accurately computed for wavelengths of 400 and 750 nm passing through a water drop at 0 Celsius. Calculation

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Reference Atmospheric Optics

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  • "Secondary Rainbow". Atmospheric Optics. Accessed on May 27, 2024.

  • "Secondary Rainbow". Atmospheric Optics, Accessed 27 May, 2024

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