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Single wavelength (monochromatic light)
The Mie algorithm models all of the "traditional" scattering processes caused by a spherical drop of water, such as external reflection, multiple internal reflections, transmission and surface waves.
The MiePlot program can produce graphs of the intensity of scattered light as a function of scattering angle, where 0° implies forward-scattering (i.e. in the original direction) and 180° implies back-scattering (i.e. back towards the source of the light).
Fig. 1 MiePlot calculation of intensity for unpolarised red light (wavelength = 0.65 µm, refractive index = 1.33257) for water drops of radius r = 0.1, 1, 10, 100 and 1000 µm
Classical geometrical optics (as described by Descartes and Newton) show that the primary rainbow is due to light which has been reflected once within a raindrop, whereas the secondary rainbow is due to light suffering two internal reflections. Geometrical optics indicates that these rainbow angles are defined solely by the refractive index of water. For a wavelength of 0.65 µm, the refractive index of water is 1.33257 which implies rainbow angles of 137.8° and 129.4°. However, Fig. 1 shows that the appearance of rainbows depends on the size of the raindrop and that the rainbow angles are not well defined for small drops.
The maxima between 170° and 180° for r = 10 µm produce the glory or circular rings around the anti-solar point (i.e. around the shadow of your head - or more frequently around the shadow of an aircraft as shown here). Similarly, the individual maxima at angles below 10° produce circular rings (corona) often seen around a cloud-covered moon.
Although scattering of light by an homogeneous sphere may seem to be a simple process, the graphs of Mie scattering are not easy to understand. Fig. 1 was calculated for unpolarised light, whereas Fig. 2 below shows separate curves for perpendicular and parallel polarisations.
Fig. 2 Mie calculation of scattering by a water drop of radius 10 µm of red light of wavelength = 0.65 µm (for perpendicular and parallel polarisations) using an angular resolution of 0.1°
Are the intricate wiggles in Fig. 2 merely mathematical curiosities? Or do they have a physical basis? The following pages use the Debye series to assist in understanding the processes involved in Mie scattering.
Page updated on 16 June 2003
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