Light refraction in the Earth's atmosphere IV. The rainbow.
DOI:
https://doi.org/10.31349/RevMexFis.72.031301Keywords:
Planetary atmospheres; light refraction; rainbowAbstract
We approach the study of the rainbow with two primary objectives: 1) to analyze the explicit dependence of the intensity and angular position of the first-order rainbow on different parameters, critically, water temperature; 2) to compare the results of geometric optics with those derived from wave theory. To achieve this, we implemented a discretization method to circumvent the obstacle posed by geometric optics, where the cross-section, and thus light intensity, diverges at the minimum deviation angle. Wave phenomena were incorporated using the Airy approximation. Through calculations spanning a broad range of parameter values, we derived analytical expressions that efficiently compute both the light intensity at the first-order rainbow’s peak and its angular position, as functions of light wavelength, drop radius, and water temperature.
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Copyright (c) 2026 A. Cruzado, A. Cesanelli, C. A. Paola
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