Abstract

This paper is concerned with the determination of the shape of a drop of water from the angular location of the cusped rainbow. This approach was stimulated by the recent discovery¹ of novel diffraction catastrophes in the rainbow region of horizontally illuminated spheroidal drops. Hyperbolic-umbilic and cusp catastrophes arise because, in addition to the usual set of equatorial rays, skew rays contribute to the scattering near the horizontal plane. The type of scattering depends on the drop’s axis ratio q = D/H where D is the diameter in the equatorial plane and H is the diameter along the vertical symmetry axis. An umbilic focal section was observed when q ≃ 1.31. Nye² has calculated this critical value from the condition that two infinitesimal-skew rays merge with two equatorial rays at the rainbow angle θ_R ≃ 138°. The cusp in the unfolded catastrophe occurs where the skew rays merge with a single equatorial ray having a scattering angle θ > θ_R. Ray tracing formalism was used to relate q to the θ of the cusp. This calculation was confirmed by observations with q from 1.21 to 1.37 and D ~ 1 mm.

© 1985 Optical Society of America