Please, show me the steps. This image shows oil floating in the Gulf of Mexico n

Question

Please, show me the steps.

This image shows oil floating in the Gulf of Mexico near Orange Beach, Alabama, three months after the BP (Deepwater Horizon) oil spill. Determine the first 3 minimum film thicknesses which would result in the cancellation (destructive interference) yellow light (590 nm), which produces the prominent blue you see in the image. noil = 1.40 nwater = 1.33 One of these film thicknesses produces a strong reflection (constructive interference) of blue light (460 nm - 480 nm). Which one?

Explanation / Answer

Part A)

Ther formula for destructive interference in this example is 2nt = m(wavelength)

Apply the formula for m values of 1, 2, and 3...

2(1.40)(t) = (1)(590 X 10^-9)

t = 2.11 X 10^-7 m (211 nm)

2(1.40)(t) = (2)(590 X 10^-9)

t = 4.21 X 10^-7 m (421 nm)

2(1.40)(t) = (3)(590 X 10^-9)

t = 6.32 X 10^-7 m (632 nm)

Part B)

For constructive interference, the formula changes to
2nt = (m + .5)(wavelength)

We need to try all three of those above thicknesses using an m value of 0, then 1, the 2, etc until we find the answer

2(1.4)(2.11 X 10^-7) = (.5)(wavelength)

wavelength = 1.18 X 10^-6 m so that will not work

2(1.4)(4.21 X 10^-7) = (.5)(wavelength)

wavelength = 2.36 X 10^-6 m so that will not work

2(1.4)(6.32 X 10^-7) = (.5)(wavelength)

wavelength = 3.54 X 10^-6 m so that will not work

Continue to do trial and error until you come up with an m = 2 value for a thickness of 4.21 X 10^-7...

2(1.4)(4.21 X 10^-7) = (2.5)(wavelength)

wavelength = 4.72 X 10^-7 m which is 472 nm

Thus the answer is the 421 nm wavelength

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