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
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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).
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.
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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