Look down on the rainbow

I told my kids that it is possible to see a whole-circle rainbow from an airplane. My son, Jon asked how high do you have to be to see a "whole" rainbow? Is a mountain high enough? -Jon K., age 11, Albuquerque, NM

You have to be high enough to look down on the rainbow so that sunlight, beaming in from behind, shines through raindrops falling below you. Then you can see the whole circle rainbow.

Look 42 degrees up and around to see a rainbow.  Drawing courtesy of Beverly Land, Unidata Program Center

Height, in itself, "...is not the critical condition for you to see the complete circular rainbow," says Robert Greenler, physics professor emeritus at the University Of Wisconsin, Milwaukee. Rather, it is your height with respect to the falling raindrops. "You can see (almost) the complete rainbow while standing in your backyard looking into the spray from the garden hose you are holding in your hand."

Rainbow reflected in Rabbitkettle Lake, NWT, Canada. Photo courtesy of Corel Corporation.

Each rainbow you see is unique to you and centered on your eyes so all rainbows form a circle centered on a point marked by the shadow of your head (called the antisolar point). To see light from the top of a rainbow, you look up at an angle of 42 degrees. To see light from the sides of the arc, you look over 42 degrees. To see light from the bottom of the rainbow, you look down 42 degrees. Of course, if the ground is in the way, you won't see the bottom of the circular bow.

The necessary conditions, says Greenler, for seeing a rainbow is: water droplets in those directions and the Sun lighting those drops. Usually the ground gets in the way and blocks water and light from reaching the lower part of the circle. See second figure. But not always. Zooming along in an airplane, you can see a whole circle rainbow because there are sun-lit drops everywhere. Looking at your garden hose spray you can see most of the rainbow circle but not the bottom part shaded by your body.

However, a mountain won't work for a full circle. "On a mountain peak-no matter how high," says Greenler, "droplets on the part of the circle below the antisolar point will be shaded by the mountain."

(Answered March 6, 2002; updated June 5, 2009)

Further Surfing:

While looking out of an airplane window, I often see a circle of colors with the shadow of the airplane at its center. What is it?

How a full-circle rainbow looks

What causes a rainbow?

I saw a lovely rainbow recently. The sky just inside the bow seemed brighter than the sky outside the bow. Why?

Why are the colors in the second rainbow backwards?