The reflection and refractions that cause a primary rainbow. Image courtesy of NASA
A rainbow almost seems like a magical phenomenon: Colors splayed across the sky in infinite subtlety and dazzling luminosity — it would be spectacular even without the pot of gold. But what causes the rainbow?
The Physics Of a Rainbow
A rainbow is caused by the prism effect of a water droplet. When light travels from one medium into another in which its speed is different, the light ray is bent; the amount of bending is inversely proportional to the wavelength.
The speed of light in a vacuum is about 3.00 x 108 meters per second. In air, it is a tad slower, but the approximation still holds. In water, on the other hand, the speed of light is much slower — about 2.25 x 108 meters per second.
When a ray of light encounters a water droplet, light entering the droplet is bent (refracted), and the colors are separated. The light then strikes the rear of the droplet and is reflected, then is refracted again when it exits the drop. An observer in the right place sees that fabulous arc of color.
The separation of colors is reversed upon reflection. The first refraction puts the long wavelength red on the inside, but the reflection reverses the spectrum and the second refraction separates the colors even more. The result is that we see red on the outside of the one-reflection rainbow, called the primary rainbow.
How Does A Double Rainbow Work?
If the observer is in the right place with respect to the water droplets, a light ray that bounces twice within the drop can create a secondary rainbow outside the first. Since each reflection causes the colors to be reversed, the second rainbow appears to have red on the inside and blue on the outside.
Each time light hits the raindrop-air interface, some of the beam is refracted and some reflected. So the secondary rainbow appears dimmer, as additional light is lost in the second reflection.
Alexander’s Dark Band
Approximately 1800 years ago, Alexander of Aphrodisias (the Greeks had a way with names) noticed that when there was a double rainbow, the band between them appeared darker than the rest of the sky. We appropriately call this Alexander’s Dark Band, though Alexander had no idea what caused it.
The angle made by the line from an observer to the center of a primary rainbow and a line from the observer to the rainbow’s arc is 42°. The comparable angle of the secondary rainbow is 50°.
Between these angles, no light can be scattered to the observer by primary or secondary reflections. Since light can be scattered from this region by other reflections and refractions, the band is not completely dark.
Higher Order Rainbows
Theoretically rainbows could be produced by any number of reflections inside a raindrop. However, the three and four reflection rainbows occur between the observer and the sun, which makes them virtually impossible to see. After that, they are so faint as to be undetectable by the human eye under any circumstances.
Best Conditions For Viewing A Rainbow
Rainbows are fairly rare because they require atmospheric conditions that don’t commonly exist. There must be sun shining on raindrops; there can be no obstructions between the sun and the raindrops, or between the raindrops and the observer.
In the middle latitudes, rainbows most commonly occur in the evening, after rain has passed from west to east and the weather has started to clear. The sunlight has an unobstructed path to the rain, and the observer has a clear view.
Can We See A Full Circle Rainbow?
A rainbow could make a full circle if the earth didn’t get in the way. From an airplane it is fairly common to see the full circle of a rainbow.
Other Applications Of The Rainbow Phenomenon
One of the most powerful tools astronomers have is the prism, with which they separate the color spectra of stars and galaxies. Of course, water is not the preferred medium. Solid prisms are much easier to handle; any transparent material such as glass works well.
By separating starlight into its constituent wavelengths, astronomers can determine, among other things, how fast a star or galaxy is moving and what trace substances it contains.
But even without practical value, a rainbow would still be as exquisite as it is ephemeral.
© Copyright 2014 Jon Plotkin, All rights Reserved. Written For: Decoded Science
Apparently we had dozens of double rainbows around Colorado over the past few days so I’ve been passing this article around again-fascinating!
It’s interesting that you mention Alexander’s Dark Band, while getting the mechanism (you said refraction separates the colors) of the rainbow and the reason for the reversal of colors in the secondary rainbow (reflects reverses images) wrong. Its interesting, because Alexander’s Dark Band explains exactly what is wrong.
A rainbow is not just an arc in the sky, it is a full circle. You see each color of light reflected everywhere from the horizon, up to the colored band you see. But each color is much, much brighter at the very top of its circle, and then it drops out.
So the red arc you see is the only part that is a single color, because it is outside of the circle produced by all the other colors of light. The violet arc is a combination of all colors of light. But the violet light is brighter than the rest, so you perceive violet. However, there is no “inside edge” to this arc – it fades to white as the violet light ceases to be brighter than the rest of the colors. This mixing does not occur outside the rainbow, so the sky appears darker there. But the physical phenomenon is that the inside is brighter.
The same thing happens with the secondary rainbow. But its circles are centered on the sun, behind you when you see the rainbow, and they wrap all the way around the zenith so that you see the effect in the same direction as the primary rainbow. Red is still on the “outside” of this bow, but “outside” is down.
Fascinating about the complete rainbow circle. I never thought of this possibility. But then, I’ve only ever ridden one plane (and I don’t want to ride any more).
Great article! I’ve never heard of Alexander’s Dark Band, but I know I’ve seen it and wondered…
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