Influence of refractive index gradients within droplets on rainbow position and implications for rainbow refractometry

Rainbow refractometry allows the determination of the refractive indices of droplets if a homogeneous refractive index can be assumed throughout the whole droplet. The influence of gradients on the angular position of the rainbow was examined for refractive index distributions with constant gradients and for distributions as they occur during cooling, heating and burning of droplets. Geometrical optics were used to determine rainbow positions. For a given value of refractive index at the surface, the rainbow position is in many cases a measure for the gradient itself. It was found that information obtained for constant gradients can often be used in cases with more complex distributions, which are found, for instance, for droplets undergoing heat-transfer processes. Significant errors may be obtained only for a very short initial phase of the process. Experimental results obtained with monosized droplet streams, which confirm theoretical predictions of the influence of gradients on the rainbow position, are presented.