Rainbows are formed when light strikes raindrops and is reflected and refracted as shown in the figure in the attached document. The figure shows a cross section of a spherical raindrop. The Law of Refraction states that (sin a) / (sin b) = k where k = 1.33 (for water).
The angle of deflection is given by D = pi + 2a - 4b.
A) Use a graphing utility to graph
D = pi + 2a - 4 sin-inverse(1/k sin a), 0 <= a <= pi/2
B) Prove that the minimum angle of deflection occurs when:
cos a = square root of [(k^2 - 1) / 3]
C) For water, what is the minimum angle of deflection, Dmin ? (The angle (pi - Dmin) is called the rainbow angle.) What value of a produces this minimum angle? (A ray of sunlight that strikes a raindrop at this angle, a, is called a rainbow ray.)
Please show detailed working.
Please refer to the attachment for full solution, with diagrams and equations.
(A) Deflection angle in radians is given as (D) and is given by (1).
D = п - 2α - ...
Law of Refraction, Rainbows, and Raindrops are exemplified.