RAINBOW       A Monte Carlo Simulation of a Rainbow
     Imagine a large number of of parallel rays hitting a spherical
     rain drop. For each ray we plot a single point of light in accordance
     with the laws of reflection and refraction. For each ray of light we
     randomly choose a color that will be seen by an observer once it has
     been refracted & reflected either resulting in a point of light in
     the primary or secondary rainbow. Since we are randomly assigning a
     color from the spectrum to a ray, the process is using a Monte Carlo
     simulation. In order to get the angles correct we use the refraction
     index of the colored light for the mediums air and water. This also
     determines the placement of the corresponding dot of light in our picture.
     The crucial line of code is the expression for N. By changing this
     line we can simulate rainbows in various mediums.
 INPUT:  ptlimit = number of point (rays) to use in the simulation.
         (If no input is specified 10,000 are used.)
 OUTPUT: primary and secondary rainbow arcs
      Original source: "Monte Carlo Computer Simulation of a Rainbow", by
      Donald Olsen, et al., The Physics Teacher, April 1990, pp. 226-227
      This was the result of an NSF summer program involving eighth and ninth
      grade students. The original program was written in Applesoft Basic.
     David R. Hill, Mathematics Dept., Temple Univ.
     Philadelphia, PA. 19122    Email: dhill001@temple.edu