Submodule 4: Rainbows Page 4
Steve Beeson, Arizona State University

Why is it a bow?

If we look away from the sun, the shadow of our head on the ground marks the point called the antisolar point, where the sun is directly opposite of us. If the sun is in the sky, the antisolar point is below the horizon. If the sun has set, the antisolar point is above the horizon.

What does this "antisolar point" stuff mean? All it is telling us is the direction of the sun and where we can expect the rainbow to form.

What we have, then, is a block of raindrops being front-illuminated by the sun, refracting the light into its various colors, and reflecting those colors back. The important thing to notice is that the red light gets refracted back at 42 from our antisolar line, and the blue light gets refracted back at about 40 from our antisolar line.

That is, every raindrop within 42 of the antisolar line is reflecting red light back to our eyes. If we look at every raindrop that is 42 from this line, what shape are we seeing?

If we look at every raindrop within about 40 of the antisolar line, we would see a circle of raindrops centered on the line. Unfortunately, the horizon gets in the way of most of the rain, so we only get to see an arc or a bow; however some people have reported seeing full rainbows from airplanes and mountain-tops.

Remember that the rain is falling not in a flat sheet, but in varying distances from you. This causes the "rainbow circle" to be formed at varying distances, also. What shape is made by circles at varying distances from an apex (in this case, your eye)?

So we find that the raindrops that contribute to your rainbow all lie on a cone with its apex at your eye. In scientific jargon, we might say:

The rainbow is an optical phenomenon caused by the refraction and reflection of light by the locus of raindrops between 40.6 and 42 of the observer's antisolar line.

Fortunately, we don't need to be that scientific to understand the nature of a rainbow...

One last thing to remember: when you see a rainbow, you are looking at the collected light from many many raindrops which, for a fleeting moment, collectively produce a "cone of color" with its apex at your eye. If you move to the left or the right, you are looking at new raindrops, and hence, a new rainbow!

If you are admiring a rainbow with a friend, you are both seeing different rainbows.

Each rainbow is your own.

"...I once saw two rainbows in the sky. How did that happen?"

Why is it brighter inside the rainbow?

Light & Optics
Submodule 4
PiN Homepage

Double Rainbows
Inside Rainbows

Copyright &copy1995
Steve Beeson, Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287