
NEWTON, Ask A Scientist!
Name: Lee
Status: educator
Age: 50s
Location: N/A
Country: N/A
Date: 10/31/2004

A friend of mine was visiting his young granddaughter and they viewed a rainbow together. Her question to him was not about the colors but was fascinating to me for such a young observer. She asked "Why is a rainbow curved and why is it in a continuous curve and not in small sections?" The grandfather seeks help and I would love to see this myself. The idea that light is broken down in passing through raindrops which are basically spherical may be part of this but somehow it seems very incomplete.

The reason a rainbow is a smooth curve is because it is the *angle* between the light incident on a raindrop, and the light exiting the raindrop, that determines what color is seen. And, as you note, it also depends on the fact that raindrops are, on average, roughly spherical. The path from sun to raindrop to viewer's eye includes the angle, and all the raindrops located so that the angle has a particular value, will contribute to a particular color of the rainbow. This might be difficult for a child to visualize, but it is a simple geometrical notion that you can demonstrate with a coat hanger.

Here is a maybe more detail than you really want about how it works:

First, some background: a ray of light that hits the middle of the raindrop is partially reflected and partially transmitted. The reflected part goes back directly toward the source; the transmitted part goes through the raindrop and is partially reflected at the back surface. Again the reflected part goes back directly toward the source; the transmitted part leaves the raindrop and we don't care about it anymore. That ray that reflected from the back surface is now heading back toward the front surface, where the partial-reflection thing will happen again -- many times, in fact. On each round trip, some light will be transmitted through the front surface back to the source.

Second bit of background: What if the light ray hits off center? Then things get very interesting. First, the surface of the raindrop acts as a prism, since the light is incident at an angle, and the light will be refracted (its path will be bent) as it passes through the surface. Second, the first reflection from the back surface will not be in the same place as the second reflection from the back surface; the light will sort of bounce around within the drop, reflecting here and there in a very predictable manner and sequence.

Third bit of background: each reflection from the back surface will make its own rainbow. Normally, you can only see the first-reflection rainbow, and maybe a faint suggestion of the second-reflection rainbow (at a different angle).

Fourth bit of background: The angle through which a light ray is bent as it passes through the air-water surface depends on the index of refraction of the water (and the air). The index of refraction of water is different for different colors of light. This is because electrons in the water molecules are tuned, like guitar strings, and a light ray tries to vibrate them at the frequency (color) of the light ray. Light rays that are nearer in frequency to the electron's "tune" are affected differently -- i.e., they see a different index of refraction -- i.e., they are slowed down by a different amount, and therefore refracted by a different angle -- than light rays farther away in frequency.

So a light ray hitting the raindrop off center will be refracted, and part of it will exit the raindrop at an angle that depends on how off-center the incident ray was. In fact, as the ray hits further and further off center, the exiting ray will make a greater and greater angle with the incident ray -- up to a point. There is a maximum exit angle, which corresponds to a certain off-center distance, and the exiting light is concentrated near this maximum angle, because the variation of exit angle with off-center distance is smallest near this angle. You can demonstrate this with a laser and a cylinder of something clear. The maximum exit angle depends on the color of light because the refraction angle generally depends on the color.

Tim Mooney

I think Ask-A-Scientist has an answer to this one:


Todd Clark, Office of Science
U.S. Department of Energy

This was answer I wrote on Aug 22, 2002. I had to search the Argonne archives to find it; (I just did not want to type it all again). Anyway, I hope this helps answer your friend's granddaughter.

Martha Croll

Yes your instincts are correct to suspect that there is "something more going on". The "explanation" you asked for sent me on a search, and the answer is a bit complicated and long to give here. However, the good news is, there is a magnificent web site that walks through the "curvature question" and several other properties of rainbows that you will (read that: I did) find very interesting and enlightening.

Check out: http://my.unidata.ucar.edu/content/staff/blynds/rnbw.html?printer

Vince Calder

Click here to return to the Physics Archives



Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory