Application of vector ray tracing to the computation of Mobius shifts for the primary and secondary rainbows

摘要

The Mobius approximation for the primary rainbow and the Konnen approximation for the secondary rainbow have been modified to yield consistent predictions of the Mobius shift of the top and bottom rainbows, respectively. The applicability ranges of the Mobius and Konnen approximations are investigated by comparison to vector ray tracing (VRT) simulations. For the primary rainbow, these results indicate that the Mobius approximation is valid for spheroidal water droplets (m = 1.333) in the range of aspect ratios 0.98 <= a/c <= 1.02. For the secondary rainbow, the Konnen approximation predicts the Mobius shift well for spheroidal water droplets within the range 0.99 = a/c = 1.01. For a spheroidal droplet with side-on incidence, the difference between the approximations and VRT simulations are discussed. Furthermore, the dependence of Mobius shifts on the relative refractive index of droplet is discussed. (C) 2015 Optical Society of America