After a hard rain, you walk out into the parking lot and notice an oil sheen on

Question

After a hard rain, you walk out into the parking lot and notice an oil sheen on top of a puddle of water. When viewed from directly above, the light reflected off the puddle is a bright red which you estimate to be a wavelength of 680 nm. The index of refraction of water is nwater = 1.33 and the index of refraction of the oil is noil = 1.47.

a) Does light reflected off the top of the oil have a phase shift? Yes/No.

b)Does light reflected off the bottom of the oil have a phase shift? Yes/No.

c)What is the minimum thickness of the oil?

d)What wavelength of light is transmitted into water most effectively?

Explanation / Answer

First we can find the thickness

2nt = (m + .5)(wavelength) for the bright red

2(1.47)(t) = (.5)(680 X 10^-9)

t = 1.157 X 10^-7 m

Then apply

2nt = m(wavelength) for the transmitted light

2(1.47)(1.157 X 10^-7) = 1(wavelength)

wavelength = 3.4 X 10^-7 m which is 340 nm

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