# Problem: An oil tanker spills a large amount of oil (n = 1.45) into the sea (n = 1.33).A. If you look down on the oil spill from overhead, what predominant wavelength of light do you see at a point where the oil is 380nm thick? What color is the light?B. In the water under the oil slick, what visible wavelength (as measured in air) is predominant in the transmitted light at the same place in the slick as in part A?(air refractive index = 1.00029)(oil refractive index = 1.45)(water refractive index = 1.33)

###### FREE Expert Solution

This problem involves the interference of light in thin films. It is because the oil forms a film on top of the water. We'll need several equations from thin-film interference.

Constructive interference (for reflected light):

$\overline{){\mathbf{2}}{\mathbf{\eta }}{\mathbf{t}}{\mathbf{=}}{\mathbf{\left(}}{\mathbf{m}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\right)}}{\mathbf{\lambda }}}$

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###### Problem Details

An oil tanker spills a large amount of oil (n = 1.45) into the sea (n = 1.33).

A. If you look down on the oil spill from overhead, what predominant wavelength of light do you see at a point where the oil is 380nm thick? What color is the light?

B. In the water under the oil slick, what visible wavelength (as measured in air) is predominant in the transmitted light at the same place in the slick as in part A?

(air refractive index = 1.00029)

(oil refractive index = 1.45)

(water refractive index = 1.33)