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In article <1992Jul20.224509.15546@fs7.ece.cmu.edu> snyder@henry.ece.cmu.edu (John Snyder) writes:
>
>So, in simple form, what is the correct explanation (including the double
>and triple rainbows)?

If it were simple, it would not be a problem of such long and interesting 
history.  But I will try anyway.  I think a good optics book will discuss 
it, and it can also be found in scattering theory books because of its
role in certain nuclear physics phenomena. 

What happens is that a light ray entering a (assume spherical) drop is 
first refracted towards the normal, reflected from the inside, then 
refracted away from the normal as it leaves.  If you follow a large 
number of rays hitting a drop a different places, you will observe a 
curious phenomenon: there are angles where no rays come out, and there 
is an angle where many rays appear to pile up as they all come out in 
the same direction.  This is the rainbow angle, and leads to a bright 
band with a sharp edge (more or less, this is where the Airy functions 
and numerical work comes in) leading to a dark region.  A second bright
band then appears after the dark region, as a result of TWO reflections 
inside the drop.  There are also supernumerary arcs in the dark region 
between the bows, but these are fainter than the second bow.  

You can convince yourself of some of this by working in 2-D with a 
circle as the raindrop.  It is rather convincing if you are careful. 

The color occurs because water is dispersive and hence the rainbow 
angle depends on color.  The second bow is reversed for reasons that 
one can see only by working out the angles themselves, but it turns 
out that the angles of the first and second bow move away from the 
common center dark region as the wavelength changes. 

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)