Generalized tertiary rainbow of slightly oblate drops: observations with laser illumination

Abstract

Oblateness in drops has been shown to produce caustics in the farfield scattering that are more complicated than the ordinary rainbow [1-7]. The complicated caustics generated are examples of "diffraction catastrophes" involving the coalescence of more than the two rays present for the usual Airy caustic [8,9]. Such diffraction catastrophes produced by scattering from oblate drops of water have been referred to as "generalized rainbows" [2,7]. While the analysis of such caustics is relevant to understanding complexity in wave propagation [8-11]. consideration of the scattering by oblate drops is helpful for anticipating whether or not generalized rainbows are likely to be visible in sunlit raindrops. The situation usually considered is the one which has the greatest symmetry: horizontal illumination of an oblate drop having a vertical symmetry axis. Generalized rainbows occur because of vertical focusing within the drop which causes the vertical curvature of the outgoing wavefront to vanish in the equatorial plane. Let D be the diameter of such a drop in the equatorial plane and let H the height. A relevant question is whether the values of the aspect ratio q = D/H required to produce the vertical focusing are sufficiently close to unity so as to be present for naturally falling raindrops. Naturally falling drops are ordinarily only slightly oblate because of the flow of air past the drop [12]. Previous laboratory observations and calculations indicate that for rays having two or three internal chords (corresponding to primary and secondary rainbow mechanisms), the required values of q are so large as to make their natural occurrence extremely rare, if ever [3-7]. It was calculated and observed that for drops having 6 chords, a bright complicated caustic was produced for q near 1.08. It was also predicted that cusps would be present for even smaller q as part of the unfolding of an axial glory caustic (as has been observed for bubbles in water [11]).