RAINBOW SCATTERING BY A CYLINDER WITH A NEARLY ELLIPTIC CROSS-SECTION

We both theoretically and experimentally examine the behavior of the f irst-and the second-order rainbows produced by a normally illuminated glass rod, which has a nearly elliptical cross section, as it is rotat ed about its major axis. We decompose the measured rainbow angle, take n as a function of the rod's rotation angle, into a Fourier series and find that the rod's refractive index, average ellipticity, and deviat ion from ellipticity are encoded primarily in the m = 0, 2, 3 Fourier coefficients, respectively. We determine these parameters for our glas s rod and, where possible, compare them with independent measurements. We find that the average ellipticity of the rod agrees well with dire ct measurements, but that the rod's diameter inferred from the spacing of the supernumeraries of the first-order rainbow is significantly la rger than that obtained by direct measurement. We also determine the c onditions under which the deviation of falling water droplets from an oblate spheroidal shape permits the first few supernumeraries of the s econd-order rainbow to be observed in a rain shower. (C) 1998 Optical Society of America.