Abstract
With the aim of building a more precise mathematical model of better predictability for the formation of the supernumerary rainbow and fogbow and seeking a clearer and more elaborate physical interpretation, this paper examines the relationship between different rainbow patterns and droplet sizes through both analytical derivation and numerical simulation and develops a much more detailed model beyond previous explanations. From Newton’s geometric model of optics to Young’s wave model, the paper first establishes a solid foundation for the understanding of the formation of the rainbow in nature and through human vision, and then goes on examining the interferences of light, finally applying the model in reality for a better understanding of complex rainbow phenomena, with additional analysis on an unexpected finding about the correspondence of maximum view angle and shortest light path through hypothetical explanation based on the principle of least time and simulation of an elliptical droplet.
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