Figure 57.4: Scattering angle vs. impact parameter for the primary and secondary rainbows. (After Nussen-
zveig,Scientific American, April 1977.)
light rays hitting the drop at around this impact parameter will be scattered in the same direction, and this is
where the rainbow will appear. According to calculations, light rays hitting the drop with an impact parameter
of 0.86 of the drop radius will have a scattering angle of 138 ı, which is the rainbow angle for the primary
bow.
Similarly, the curve for the secondary bow (two internal reflections) has a maximum at about 0.95 the
radius of the drop. Therefore many light rays light hitting the drop with an impact parameter around 0.95 of
the drop radius will scatter at about the same angle, which is rainbow angle of the secondary bow, 130 ı.
57.5 Alexander’s Dark Band
As seen in Figure 49.4, there is no impact parameter for either the primary or secondary bow that will lead to
light being scattered between 130 ıand 138 ı. This results in a dark band between the primary and secondary
bows, known asAlexander’s dark band(Fig. 57.1).