Question

A certain grade of crude oil hasan index of refraction of 1.15. A ship accidentally spills 2.00 m³ 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 550 nm normally incident on it, how much surface area of the ocean does the oil slick cover? Assume the index of refraction of the ocean water is 1.34.

Answer 1

this is a thin film interference problem oil on water

the formula for that kind of interference is

2ne=k*lambda for constructive interference or

2ne=(2k+1)*lambda/2 for destructive interference

here K is the order or interference equal to 0, 1,2,3,4,5,6

the problem says that we are in the first order of maximum interference then we use the first equation with k=1

so 2ne=lambda

where we isolate e

e=lambda/2n

e is the thickness in m of the oil film, n=refraction index of the oil, lambda is the wavelength in meters

SO

e = (550*10^-9)/(2*1.15) = 2.39*10^-7 m

If e is known and we have the total volume of oil dumped, it is easy to find the surface of oil spill

S=Volume/e

= 2/(2.39*10^-7)

= 8.36 x 10⁶ m²