Rainbows are created when sunlight of different wavelengths (colors) is refracted and reflected in raindrops. The...
Math 20 - Calculus I $4.2 - Extra Credit Applied Project: The Calculus of Rainbows Show your work! Good luck! (40pts) Rainbows are created when raindrops scatter sunlight. They have fascinated mankind since ancient times and have inspired attempts at scientific explanation since the time of Aristotle. In this project we use the ideas of Descartes and Newton to explain the shape, location, and colors of rainbows. 1. The figure shows a ray of sunlight entering a spherical raindrop at...
Problem 2 Show that for an index ofrefraction k that D(a) is minimized when sin α- 4 Use this to obtain p- arcsin to obtain ß arcsinand fil in the following table. 4-k2 3k2 a in degrees B in degrees R(a) in degrees Color Red Orange Yellow Green Bluc Indigo Violet 1.331 1.332 1.333 1.335 1337 1.340 1.344 The values of R(a) you obtained in the table accounts for the various color bands that appear in the rainbow as sunlight...