8—Multivariable Calculus 240only a few percent of the light is reflected and the rest goes through. The cross section should be multiplied by
this factor to be complete. The detailed equations for this are called the Fresnel formulas and they tell you the
fraction of the light transmitted and reflected at a surface as a function of angle and polarization.
This is far from the whole story about rainbows. Light is a wave, and the geometric optics approximation
that I’ve used doesn’t account for everything. In fact Eq. ( 29 ) doesn’t apply to waves, so the whole development
has to be redone. To get an idea of some of the other phenomena associated with the rainbow, see for example
http://www.usna.edu/Users/oceano/raylee/RainbowBridge/Chapter8.html
http://www.philiplaven.com/links.html
8.15 3D Visualization
Wrapping your mind around three dimensional objects is a practiced skill, one that takes time to master. For an
interesting way to enhance this ability, I recommend the Java Applet
http://www.ausserfern.at/pbeck/blockout/