Analysing the secondary rainbow
(using the Debye series)

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)    Fig. 2   Secondary rainbow:  Debye series 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