Abstract: Mie theory offers an exact solution to the problem of scattering of sunlight by spherical drops of water. Until recently, most applications of Mie theory to scattering of light were restricted to a single wavelength. Mie theory can now be used on modern personal computers to produce full-color simulations of atmospheric optical effects, such as rainbows, coronas, and glories. Comparison of such simulations with observations of natural glories and cloudbows is encouraging.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Abstract: The scattering of light from homogeneous spheres might be considered to be a trivial problem because rigorous solutions, such as Mie theory, were developed almost 100 years ago. Nevertheless, full-colour simulations of atmospheric optical effects, such as rainbows, coronas and glories, reveal several intriguing issues. Calculations using the Debye series can help us to understand the scattering mechanisms causing specific effects: for example, the atmospheric glory seems to be caused by light rays that have suffered one internal reflection within water drops.

Abstract: Mie theory can be used to provide full-color simulations of atmospheric glories. Comparison of such simulations with images of real glories suggests that most glories are caused by spherical water droplets with radii between 4 and 25 µm. This paper also examines the appearance of glories taking into account the size of the droplets and the width of the droplet size distributions. Simulations of glories viewed through a linear polarizer compare well with the few available pictures, but they show some features that need corroboration by more observations.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Abstract: Mie theory can be used to generate full-color simulations of atmospheric glories, but it offers no explanation for the formation of glories. Simulations using the Debye series indicate that glories are caused by rays that have suffered one internal reflection within spherical droplets of water. In 1947, van de Hulst suggested that backscattering (i.e., scattering angle theta = 180°) could be caused by surface waves, which would generate a toroidal wavefront due to spherical symmetry. Furthermore, he postulated that the glory is the interference pattern corresponding to this toroidal wavefront. Although van de Hulst’s explanation for the glory has been widely accepted, the author offers a slightly different explanation. Noting that surface waves shed radiation continuously around the droplet (not just at theta = 180°), scattering in a specific direction theta = 180° + d can be considered as the vector sum of two surface waves: one deflecting the incident light by 180° + d and the other by 180° - d. The author suggests that the glory is the result of two-ray interference between these two surface waves. Simple calculations indicate that this model produces more accurate results than van de Hulst’s model.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Abstract: A ray-theoretic account of the passage of light through a radially inhomogeneous transparent sphere has been used to establish the existence of multiple primary rainbows for some refractive index profiles. The existence of such additional bows is a consequence of a sufficiently attractive potential in the interior of the drop, i.e., the refractive index gradient should be sufficiently negative there. The profiles for which this gradient is monotonically increasing do not result in this phenomenon, but nonmonotone profiles can do so, depending on the form of n. Sufficiently oscillatory profiles can lead to apparently singular behavior in the deviation angle (within the geometrical optics approximation) as well as multiple rainbows. These results also apply to systems with circular cylindrical cross sections, and may be of value in the field of rainbow refractometry.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.