Some Aspects of the Optics of the Rainbow and the 
Physics of Rain 
Frreprich E. Vouz 
Blue Hill Meteorological Observatory, Harvard University, Milton, Massachusetts 
Abstract—It has hitherto usually been believed that the classic rainbow theories of 
Descartes and Airy for spherical drops completely satisfy the observations. However 
the well-known deviations of large falling drops from a spherical shape require changes 
in the rainbow angle, especially for scattering in the vertical cross section of the drop. 
Flattened raindrops of different radii cannot form a perceptible bow; this may explain 
why the interference bows are more visible at the top of the bow than towards the 
base, although their spacings do not change. 
Preliminary investigations on the oscillations of large fallimg raimdrops have been 
made. Such oscillations can result in blurring or washing out the rainbow. Rainbow in- 
tensities for measured drop size distributions have been calculated from the Airy 
theory. Since drops with radii larger than 0.2 to 0.6 mm are flattened and oscillating, 
they contribute little to the rambow. Analysis of the rainbow can therefore only give 
information about the spectrum of the smaller drops. 
Studies of the rainbow have found little place 
in modern investigations into the physics of rain; 
and yet this beautiful natural phenomenon is by 
no means as lacking in interesting problems as 
it may seem to be. The well-known classical Airy 
theory requires much modification before it can 
be applied to actual atmospheric conditions. 
Few meteorologists may know that the super- 
numerary or interference bows (if they can be 
seen at all) gradually fade as we go from the 
vertex of the bow to the horizon, but without 
any change taking place in the displacement 
from the main rainbow. Also there have been 
only two recorded observations in the past of 
vibrations in the rainbow caused by thunder. 
As this paper will try to demonstrate, the 
first phenomenon is probably connected with the 
deformation of any large raindrops, while the 
Fig. 1—A rainbow photographed by Clarke [1920] showing how the inter- 
ference bows vanish from the apex to the foot of the bow (Permission of 
Constable and Co., Ltd., London) 
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