A new, and unfortunate, oil spill has occurred of the coast of California. When

Question

A new, and unfortunate, oil spill has occurred of the coast of California. When viewed from the air above, a scientist notices a colorful rainbow of hues in the oil slick. She focuses in and uses a spectrometer to verify the wavelength of light coming from one particular spot to be 750 nm (in air).?

A. If the index of refraction of the oil is 1.20, what is the minimum thickness t of the oil slick at that spot??

B. Suppose the index of refraction of the oil instead was 1.50. What would the minimum thickness t be now??

C. Keeping the same index of refraction, noil = 1.50, we also assume the thickness of the oil is 200 nm. If a diver is underneath the oil slick looking up through the same spot that the scientist examined with the spectrometer, what is the longest wavelength ?water of the light in water that would be transmitted most easily to the diver?

Explanation / Answer

two low to high ( 1->1.2 and 1.2=>1.33) so

(m ) lambda/n = 2 d

so min thickness wehn m = 1

d = lambda/(2n ) = 750/(2*1.2)= 312.5 nm

b) now, one low to high

so (m + 1/2) lambda/n = 2d

min thickness when m = 0

so d = lambda/4n = 156 nm

c) for transmission
no lows to high

so m lambda/n = 2 d

lambda = 2 d n/m

longest means m = 1

lambda = 2 d n = 2*200*1.5 = 600 nm

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