Fig. 6 Corona: Mie calculation of scattering by a water drop of radius 10 µm of red light of wavelength = 0.65 µm |
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Fig. 6 Corona: Mie calculation of scattering by a water drop of radius 10 µm of red light of wavelength = 0.65 µm |
Fig. 6 shows scattering of red light by a water droplet with a radius of 10 µm. The maximum around 3° corresponds to the corona, which is often seen as a ring around a cloud-covered moon. Noting that the vertical axis of Fig. 6 has a logarithmic scale, the intensity of the corona is only about 3% of the intensity in the forward direction (0°). Coronas also appear around the sun, but are generally not visible because our eyes are dazzled by the brightness of the sun.
The corona is usually attributed to diffraction, but Fig. 6 does not
show the regular scattering pattern normally associated with diffraction.
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| Fig. 7 Corona: Various calculations of scattering by a water drop of radius 10 µm of red light of wavelength = 0.65 µm (perpendicular polarisation) |
Fig. 7 shows that the Debye p = 0 contribution is dominant in the forward-scattering zone (scattering angles below 5°). As noted above, the p = 0 term includes both diffraction effects and external reflection. The blue curve in Fig. 7 represents the diffraction process: it has been calculated using the following equations:
For scattering angles below about 6°, the maxima for the p = 0 term
coincide with the maxima of the diffraction term. The minima are
much shallower for the p = 0 term than for the diffraction term (because
the p = 0 term includes reflection from the exterior of the sphere).
However, note that the minima calculated using Mie theory do not coincide
with the minima of the diffraction pattern.
Fig. 8 Corona: Debye series calculation of scattering by a water drop of radius 10 µm of red light of wavelength = 0.65 µm (perpendicular polarisation) |
Fig. 8 identifies the cause of the sharp minimum at 4.3° - which
is where the red and the magenta curves cross each other. The red
curve represents the contribution from p = 0 rays (external reflection
+ diffraction) whilst the magenta curve represents p = 1 rays (direct transmission).
The black curve, which represent the vector sum of the p = 0 and p = 1
rays, has a deep minimum at 4.3°. This indicates that, in this
direction, the p = 0 and p = 1 contributions are of equal amplitude but
with a phase difference approaching 180°. As the black
curve is almost identical to the Mie curve in Fig. 7, it is also clear
that the p = 0 and p = 1 contributions are dominant in the forward scattering
zone.
MiePlot v2.0 offers the option of using the Debye series.
Page updated on 10 November 2002
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