Doubling down: What makes a double rainbow and other rainbow science
September 22, 2012
This morning north of Ludington, photo by Debbie Maglothin
It seems only fitting to follow up waterspouts with rainbows. The National Center for Atmospheric Research has an incredibly comprehensive page about rainbows. After explaining the optics behind rainbows (complete with diagrams), they delve into double rainbows:
Sometimes we see two rainbows at once, what causes this? We have followed the path of a ray of sunlight as it enters and is reflected inside the raindrop. But not all of the energy of the ray escapes the raindrop after it is reflected once. A part of the ray is reflected again and travels along inside the drop to emerge from the drop. The rainbow we normally see is called the primary rainbow and is produced by one internal reflection; the secondary rainbow arises from two internal reflections and the rays exit the drop at an angle of 50 degrees° rather than the 42°degrees for the red primary bow. Blue light emerges at an even larger angle of 53 degrees°. This effect produces a secondary rainbow that has its colors reversed compared to the primary, as illustrated in the drawing, adapted from the Science Universe Series Sight, Light, and Color.
It is possible for light to be reflected more than twice within a raindrop, and one can calculate where the higher order rainbows might be seen; but these are never seen in normal circumstances.
You may have noticed that the sky is brighter inside the rainbow above. They explain why the sky is brighter inside both single & double rainbows:
Notice the contrast between the sky inside the arc and outside it. When one studies the refraction of sunlight on a raindrop one finds that there are many rays emerging at angles smaller than the rainbow ray, but essentially no light from single internal reflections at angles greater than this ray. Thus there is a lot of light within the bow, and very little beyond it. Because this light is a mix of all the rainbow colors, it is white. In the case of the secondary rainbow, the rainbow ray is the smallest angle and there are many rays emerging at angles greater than this one. Therefore the two bows combine to define a dark region between them – called Alexander’s Dark Band, in honor of Alexander of Aphrodisias who discussed it some 1800 years ago!
Read on for much more about rainbows including supernumerary arcs, why we don’t often see rainbows in winter and even lunar rainbows! If you want to go rainbow crazy, head over to Atmospheric Optics for tons more rainbow information & photos.
See more rainbows on Michigan in Pictures. Also, I’ve added a new “science” category to Michigan in Pictures. I’ll tag past posts like the post about sundogs, rainbow-like formations you often see in winter. If anyone has a favorite, just post a comment on it mentioning that it would be a good fit for science!