Scientific- Research Quarterly of Geographical Data (SEPEHR)

Scientific- Research Quarterly of Geographical Data (SEPEHR)

Mathematics of rainbows

Document Type : Research Paper

Authors
Maryam Shafiei 1
Zahra Arzjani 2
1 Mathematical Society
2 Azad University
Abstract
The present article investigates this research question: “why rainbows are only visible between 40 to 42 degrees in a spherical drop of water?” When a ray of sunlight enters a water drop, some of the light will be reflected, some will pass through the drop and some will be refracted according to Snell law and exit the drop and create a rainbow.
Two main factors, refractive index and wave length create different colors of rainbows and play an important role in the occurrence of rainbows. Every water drop can create one of the rain bow colors in human visual range. Then, we explain why rainbows are curved.
According to the investigations performed and mathematical formulas proved, we conclude that the intensity of light rays exiting the drop from different angles is not the same, and most of the exiting colorful light make an approximately 42 degree angle with the solar radiation. Yet, this angle depends on the light color. For red to purple, this angle is about 40 to 42 degrees.
Keywords
rainbow
mathematics
Snell law
wave length
light refraction
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