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# Understanding glories: Mie theory

Glories are caused by scattering of light from small spherical drops of water - and can be simulated using the MiePlot computer program as shown in Fig. 1 - which compares the corona (centred on the forward-scattering direction of θ = 0°) and the glory (centred on the back-scattering direction of θ = 180°).

Fig. 1   MiePlot simulations of the corona (top) and the glory (bottom) for r = 10 µm water droplets

Although the sequence of colours is similar in the corona and the glory, the sizes of the rings are different and more rings can be seen with glories. When observing glories, you will see that the centre of the coloured rings (i.e. θ = 180°) is generally bright and surrounded by a darker ring.   Despite the similarities, coronas and glories are caused by completely different scattering processes.  Coronas are essentially due to diffraction of light around spherical drops of water - but the glory is much more difficult to explain. The next page How are glories formed? indicates that the glory is caused by light rays incident at opposite edges of spherical water drops: the two light rays are reflected once within the drop, thus generating surface waves which produce backscattering in directions such as θ > 170°. Interference between these two backscattered components causes the distinctive glory pattern.

 Fig. 2   Mie scattering of white light by r = 10 µm water droplets

Fig. 2 shows that the back-scattered light is dependent on polarisation.  The parallel polarised component has its maximum intensity at θ ≈ 178.6°, whereas perpendicular polarisation has its maximum at θ = 180° (where the curves for the two polarisations meet).  The coloured bars above the graph in Fig. 2 show that the coloured rings of the glory do not coincide with the peak intensity.  Hence, misleading results will be obtained if the glory is studied using calculations of scattering at a few wavelengths.  Fig. 2 is based on Mie calculations using 300 discrete wavelengths between 380 nm and 700 nm to simulate the continuous spectrum of sunlight.

It is possible to estimate the size of the water droplets by measuring the radius of the red rings in a glory.  Large rings imply small droplets, whilst small rings imply large droplets.  To a first approximation, the radius of the rings is inversely proportional to the radius r of the water droplets: for example, the 4 inner red rings appear at radii of approximately 24/r, 37/r, 56/r and 76/r (where r is measured in µm).  For example, for r = 10 µm, the innermost red ring appears at a radius of about 2.4° from the anti-solar point (θ = 180°), which corresponds to a scattering angle θ = 177.6°.

In practice, glories are usually seen against a background of white clouds.  Clouds are white because light from the sun is subject to "multiple" scattering within the clouds, in which light is scattered from one water droplet and then scattered by one or more other droplets.  Brightly coloured glories are caused by single scattering (i.e. each ray of light is scattered by a single droplet before leaving the cloud).  In effect, the finer details of glories are often obscured by the white light scattered from the clouds - but without the clouds there would be no visible glory!

Page updated on 4 July 2006

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