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The Debye series can also be used to understand the mechanisms of Mie scattering in the vicinity of the secondary rainbow.
Fig. 1 Secondary rainbow: Debyeseries calculation of scattering by a water drop of radius r = 100 µm for wavelength λ = 0.65 µm (perpendicular polarisation)

As shown in Figs. 1 and 2 above, the secondary rainbow is slightly more complicated than the primary rainbow.
The blue curve shows the contribution made by p = 3 rays (those that have suffered 2 internal reflections), whilst the red curve in Fig. 1 shows the vector sum of p = 0 rays (external reflection) and p = 3 rays.
The magenta curve in Fig. 2 shows the vector sum of p = 6 rays (5 internal reflections) and of the red curve (p = 0 and p = 3 rays). The Debye series results shown by the magenta curve are almost identical to Mie calculations, indicating that, for r = 100 µm, the p = 0, p = 3 and p = 6 rays are dominant for scattering angles between 120° and 132°.
MiePlot offers the option of using the Debye series.
Page updated on 7 September 2002
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