# Calculus Help

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I have looked high and low to figure out how to start this question. I have no clue! Any help would be great!!

Rainbows are formed when light strikes raindrops and is reflected and refracted. The Law of Refraction states that (sin alpha)/(sin beta) = k, where k equals 1.33 (for water). The angle of deflection is given by D= pi + 2 alpha -4beta.

a. Write an equation for D in terms of alpha only.

I have so far sin alpha equals ksin beta I know I use this to solve for beta to plug into the equation but not sure how to do this after this step.

b. Prove that the min angle of deflection occurs when cos alpha equals sqrt((k^2-1)/3)

c. For water, what is the min angle of deflection? (pi minus Dmin is called the rainbow angle). What value of alpha produces the min angle? (A ray of sunlight that strikes a raindrop at this angle is called a rainbow ray)

• Calculus Help -

sinβ = sinα / k
β = arcsin(sinα/k)
D = π + 2α - 4arcsin(sinα/k)

what's next?

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