How do I calculate the surface area of an oil slick?

[Mohji]

Homework Statement

A certain crude oil has an index of refraction of 1.24. A ship dumps 1.39 m^3 of this oil into the ocean, and the oil spreads into a thin uniform slick. If the film produces a first-order maximum of light of wavelength 517 nm normally incident on it, how much surface area of the ocean does the oil slick cover? Assume that the index of refraction of the ocean water is 1.34.

n1 = 1.24
n2 = 1.34
λ = 517 nm = 5.17e-7 m
V = 1.39 m^3
θ1 = 90°

Homework Equations

mλ = d*sinθ
V = π*r^2*t
A = π*r^2

The Attempt at a Solution

θ2 = arcsin(1.24/1.34) = 67.7°

mλ = d*sinθ2
d = λ / sinθ2
d = (5.17e-7 m) / sin(67.7°)
d = 5.59e-7 m

"d" is also the thickness "t" of the oil.

V = π*r^2*t = 1.39 m^3
A = π*r^2 = V / t

A = V / t
A = 1.39 m^3 / 5.59e-7 m
A = 2.49e6 m^2

Can someone explain to me what I am doing wrong here? The online assignment is not accepting the answer. Any help at all would be greatly appreciated.

 

[Adrmay]

A:You forgot to use the formula for the maximum angle of refraction,$$\sin \theta_2 = \frac{n_1}{n_2} \sin \theta_1$$Rather than simply assuming $\theta_2 = \arcsin(n_1/n_2)$.