A pair of classical rays with the same deviation through
For each deviation angle there are always two**
rays at different distances from the drop centre that have the same
Geometric optics incorrectly *** predicts
that their light combines to produce extra brightness in that direction.
quite unable to explain the bands of light and dark, supernumeraries,
inside the humble rainbow.
The same ray path pair replaced by a representation*
of light waves. Wave crests of opposite amplitude are shaded green
The rays have different path lengths. This has the result that after
they have left the drop their wave crests are not necessarily aligned
For some pairs of equal deviation rays the crests will be aligned
(in phase). Those of other pairs and ray directions will be completely
misaligned (out of phase) in the sense that crests of opposite amplitude
will correspond instead. The diagram shows an intermediate condition.
When crests having the same amplitude direction are aligned the two
waves reinforce each other and there is bright
light at that particular deviation angle. When crests of opposite
amplitude are aligned the waves cancel and there is
darkness. This is interference.****
Imagine now the ray pairs for a range of deviation angles. As the
angle changes the wave pairs alternately reinforce or cancel each
other to produce light and dark fringes. Each bright fringe is a supernumerary