Physics Photo of the Week

Double Rainbow at Soccer Game

Molly McMillen, the Warren Wilson Women's Soccer Coach, took this marvelous photo of the double rainbow at the halftime break during the women's soccer game on Wednesday, August 30, 2006.  For an excellent account of the game, see Molly's article.  I also thank Stacey Enos, athletic director at WWC, for calling my attention to Molly's photograph.  I will attempt to describe the physics of the double rainbow as requested by the WWC Atheletic Department. I have digitally enhanced this photo in order to enhance the contrast between the rainbows and the sky.  The outer rainbow is quite faint.  As a result the foreground looks a bit darker than in Molly's original photo

To explain the main primary rainbow (the bright lower rainbow) look at the diagram at right.  This shows a raindrop - yes raindrops are round.  Sunlight enters the raindrop as a multitude of rays as shown.  One ray in particular is traced through the raindrop.  This ray is bent or refracted where it enters the raindrop; it is partially reflected by the inside of the back of the raindrop; it then exits near the bottom of the raindrop.  Where the ray enters and leaves the raindrop, it is dispersed into colors - similar to the colors produced when white light shines through a prism.  For simplicity the drawing only shows the dispersion where the light exits the raindrop. Each of the myriad of sunlight rays in the drawing enters and bounces around the raindrop in a similar manner, but only the principle ray is shown.  When we see a rainbow, we see the effect of millions of raindrops.  The raindrops in the appropriate direction relative to the sunlight direction are in the appropriate position to show the blue reflected light.  The raindrops that are in the correct position to reflect red light to the observer are a little bit higher.  Thus the millions of raindrops that lie in the direction favorable to the observer create the arc of the rainbow.

The outer, fainter secondary rainbow is caused by a similar process.  One of the other sun rays enters the raindrop and is internally reflected twice rather than singly for the primary rainbow.  Because a large fraction of the light is lost at each internal reflection, the secondary rainbow is much fainter than the primary rainbow.  Conditions to see the secondary rainbows include bright sunlight and a dark cloud in the background.  This was true at the soccer game.

The photo below is a laboratory set-up of an artificial raindrop.  It consists of a water-filled spherical flask (about 10 cm diameter - much larger than a raindrop).  The flask  is suspended in front of a projector to simulate the sunlight and photographed at the proper angle.  The light from the projector enters the artificial drop from behind the camera from the left.  The light bounces and bends in the flask as in the drawing above.  The camera captures the light rays leaving the "drop" near the right-hand edge of the "drop".  Notice that the exiting light exhibits some color.  The spot just to the left of the center is partial reflection of the projector lamp by the surface of the artificial raindrop.  Over on the left side of the flask, one can see two colored spots.  At a slightly different position of the flask, the left side spots will converge into one spot.  This produces the secondary rainbow - arising from two internal reflections, which make it much fainter.
 

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