Re: Why do the colors of the rainbow occur where they do?

Remember that the water droplets act as prisms; they literally focus
the various wavelengths of light.  Different wavelengths of light have
different energies, and are diffracted (bent) at different and distinct
angles as they pass through.  The different wavelengths give rise to the
different colors we see.  Short wavelengths are the violet end of the
spectrum; long wavelengths are the red end.

Now, why do they fall into such neat bands in the sky?

It is because the light is all coming from the same direction -- the
sun.  The rays strike spherical water droplets at the same angle, and
each droplet focuses the diffracted light in the same direction.  You
only see the visible light bands appear when the light is focused in 
the right direction.