| In addition to the calculations of scattering for light of a single
wavelength, MiePlot can simulate the scattering of sunlight by combining
the results for several wavelengths.
The contributions at various wavelengths can be added together to simulate
the primary rainbow. Fig. 1 shows the result for red, green and blue light
(wavelengths of 0.65, 0.51, 0.44 µm respectively). As the refractive
index changes with wavelength, the monochromatic "rainbows" occur at different
angles: the maximum intensity occurs for red light at 138.5°, green
at 139.2° and blue at 139.6°.
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| The upper curves on these graphs represent the sum of the individual coloured "components"; whilst the colour of the upper curves depends on the relative strengths of the coloured components. For example, in Fig. 1, the upper curve is essentially red between 137° and 138° because the red component is much stronger than the green and blue components. Around 138.5°, the red and green components are of similar intensity, resulting in a yellow segment of the curve, whereas around 139° the green component is dominant - and so on. |
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| The 3 horizontal stripes above each graph simulate the primary rainbow:
the top stripe is for perpendicular polarisation, the middle stripe is
for parallel polarisation and the bottom stripe is for unpolarised light.
Note that the stripe for parallel polarisation is almost black, indicating
that the primary rainbow is strongly polarised.
Fig. 1 shows a rainbow-like pattern including supernumeraries, but Figs. 2 and 3 offer a better approximation to the "colours of the rainbow". |
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Fig. 4 Debye series calculations for scattering of sunlight from a water drop with radius of 200 µm |
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It is well known from geometric optics that the primary rainbow is due to rays that have suffered one internal reflection (p = 2) within the sphere and that the secondary rainbow is due to rays that have suffered two internal reflections (p = 3). Fig. 4 shows the results of Debye series calculations for scattering of sunlight. Note that the horizontal coloured bars above the graph in Fig. 4 show the full Mie calculation and the contributions from different ray paths - showing very clearly that the main contributions are from p = 0, p = 2 and p = 3 rays. In real life, the secondary rainbow is much weaker than the primary rainbow - but the visibility of the coloured bars in Fig. 4 depends on the characteristics of your computer display. You should adjust the brightness and contrast of your display so that the grey scale in Fig. 5 below has uniform steps in brightness between adjacent blocks - whilst ensuring that you can also see the small squares in the centre of the left and right blocks.
Fig. 5 Grey scale to assist in adjusting your computer display
Updated on 4 April 2003 |
