Rainbows, Glories, and the Scalar Field Approach

Abstract

The purpose of this study is to investigate the limitations, apart from polarization effects, of the scalar field in accounting for the phenomena of the rainbow and the glory. The scalar scattering intensity and the electromagnetic Mie scattering intensities are plotted and compared in great detail in the critical regions of the rainbow and the glory for spheres of various sizes and refractive indices. In addition chromaticity calculations based on the scalar and Mie intensities are shown and compared. It follows that the scalar field can adequately describe the rainbow. In addition, old conclusions regarding the colors of the main bow are confirmed but no supernumeraries can be expected for droplets with diameter less than 100 μ. A rainbow effect on lake surface is reported. It follows that the scalar field is inadequate to describe quantitatively the glory. It is shown that the first red ring of the glory is useless in determining droplet size, and that the Van De Hulst theory in its common form predicts larger droplet size by 10%.