The Möbius approximation for the primary rainbow and the Können approximation for the secondary rainbow have been modified to yield consistent predictions of the Möbius shift of the top and bottom rainbows, respectively. The applicability ranges of the Möbius and Können approximations are investigated by comparison to vector ray tracing (VRT) simulations. For the primary rainbow, these results indicate that the Möbius approximation is valid for spheroidal water droplets () in the range of aspect ratios . For the secondary rainbow, the Können approximation predicts the Möbius shift well for spheroidal water droplets within the range . For a spheroidal droplet with side-on incidence, the difference between the approximations and VRT simulations are discussed. Furthermore, the dependence of Möbius shifts on the relative refractive index of droplet is discussed.
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23 October 2015: A correction was made to the funding section.
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