The Story Behind That Quadruple Rainbow

Social media lit up on Tuesday as a stunning photo of what appears to be a quadruple rainbow made the rounds. Amanda Curtis took the shot while waiting on a train at Glen Cove, NY, this morning. After she posted it to Twitter, the image quickly went viral. Curtis was interviewed over the phone by Jim Cantore and Sam Champion on The Weather Channel’s “AMHQ” program. As Curtis explained: “I was waiting for my commuter train into New York City and I was outside on the Glen Cove station platform and saw two double rainbows and was just absolutely blown away by it and decided to take the opportunity to snap the picture to use for later inspiration... I was outside and my train was coming, so I think I’m good under pressure and just decided to snap it and then run after the train.”




Figure 1. Amanda Curtis interviewed this morning on “AMHQ”. Image credit: The Weather Channel.



Figure 2. The tweet that sent cyberspace into rainbow heaven today. Image credit: Amanda Curtis.


At first, I was skeptical: the photo seem to run counter to everything I knew about atmospheric optics. Multiple rainbows can form due to reflections within the same raindrops that produce a single rainbow, but each iteration produces a fainter bow. The optics that produce each type are well-known. The arc of a single rainbow extends 41° around a line that runs from the sun through the observer’s head to the opposite side of the sky (the antisolar point). The closer to sunset it is, the higher in the sky the rainbow will appear. A double, or secondary, rainbow, forms a ring around the first rainbow, with an angle of 51° from the antisolar point. Secondary rainbows are fairly unusual, though I’ve seen a few. (See a good WunderPhoto example below.)

Even more rarely seen, and often disputed, are true triple and quadruple rainbows, which would appear on the other side of the sky--surrounding the sun, instead of opposite from it, and thus much harder to see. The first-ever scientifically vetted and verified photo of a pair of tertiary and quarternary (third- and fourth-order) rainbows were captured in Germany just four years ago, with the subsequent analysis published in the journal Applied Optics in 2011. And even more recently, a photographer in New Mexico captured the exceedingly faint fifth-order rainbow, which occurs in the slightly dimmed area called Alexander’s dark band between the primary and secondary bows.


Figure 3. Example of a primary (bottom) and secondary (top) rainbow. Image credit: wunderphotographer DI85.


What happened this morning in New York was a quite different phenomenon. A good analog is this Astronomy Picture of the Day, posted by NASA in 2007. It includes a standard single rainbow (the brightest) and secondary bow (arcing around the first one, toward the left), but also visible is a third bow that seems to connect the two. NASA explains: “This [third] rainbow is likely caused by sunlight that has first reflected off the lake before striking the distant raindrops that is reflecting sunlight back toward the observer. Each of these rainbows appears to be reflected by the calm lake, although because the positions of rainbows depend on the location of the observer, a slightly displaced image of each rainbow is actually being imaged.”

When I expressed initial doubt about today’s viral image, NOAA scientist and avid photographer Paul Neiman begged to differ. Paul pointed me to the NASA photo mentioned above, and provided this compelling explanation for the Glen Cove image:

“A typical primary rainbow is caused by refraction and one internal reflection of sunlight within raindrops, resulting in a rainbow that is positioned 41 arc degrees from the anti-solar point (i.e., the point directly opposite the sun – for example, if the sun is 10 degrees above the horizon at your back, the anti-solar point is 10 degrees below the horizon directly in front of you). The refraction causes the separation of white sunlight into its component colors, with red on the outside of the rainbow and violet on the inside. The secondary rainbow, which is centered 51 arc degrees from the anti-solar point (i.e., the larger of the two bows during a typical display), involves two internal reflections of sunlight within the raindrops rather than one, resulting in a reversal of the color sequence (red on the inside and violet on the outside). We can usually only see the portion of these rainbows above the horizon, because there isn’t a sufficient density of raindrops between the observer and the ground to see the rainbow below the horizon (exceptions include full-circle rainbows viewed from locales such as airplanes and mountain tops).

“So far, so good. For the much rarer reflected-light rainbows shown in this spectacular photo, a large glassy-smooth water surface is required behind the observer. This smooth water surface reflects the sun, such that a second solar light source is generated. This reflected sun, which is located the same the number of arc degrees below the horizon as the real sun is above the horizon, creates a second primary and secondary rainbow on the opposite side of the sky from the sun, but with the center of these reflected-light rainbows above the horizon. The geometry dictates that the regular and reflected-light rainbows will join at the horizon, as this photo suggests.”

Supporting Paul’s explanation is the fact that Oyster Bay sits a few miles east of where Amanda Curtis took the photo, so the morning sun could have reflected off a nearly calm bay, as noted by The Weather Channel’s Mark Elliot, before producing the rainbows captured by Curtis in the western sky. Readings from a Wunderground personal weather station at Oyster Bay showed that winds were nearly calm early this morning.

Special thanks go to Paul Neiman and to the Weather Channel’s Matt Sitkowski and Stu Ostro for informative discussions on this fascinating image.

Bob Henson


Figure 4. Another good example of a primary (bottom) and secondary (top) rainbow, taken on the Washington coast. Image credit: wunderphotographer 50something.