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# PHYS QUESTION, need help?

An oil slick (where n = 1.78) sits on top of water (where n=1.45). The thickness of the oil slick is 555 nm. What is the visible wavelength of light that has the strongest reflection from this oil slick? This is the wavelength that would undergo constructive interference on reflection. The range of visible wavelengths is 400 nm to 700 nm. Enter your answer in nm.

A set up an Michelson interferometer using 556 nm light, ensuring that the two arms have the same length. Then, you insert a piece of glass with a thickness of 4.78 um (micrometers) and an index of refraction of n = 1.56 into one of the arms. What is the resulting phase difference between the two arms? You can assume the interferometer is in air, where n=1.00.

please and thank you

### 1 Answer

- NCSLv 71 month ago
Not really in my wheelhouse, but I'll try the first one.

The light changes phase by 180º when it reflects off the top of the film (because n_oil > n_air), but it doesn't change phase when it reflects off the bottom of the film (because n_water < n_oil). Therefore in order to get constructive interference, we need an odd number of ½ wavelengths of light to travel down and back through the oil:

N = 2t / (λ/(2n)) = 4nt / λ

should do it, where n = 1.78 and t = 555 nm and N is odd.

N*λ = 4*1.78*555nm = 3952 nm

The longer the wavelength, the fewer of them we'll need (lower N). 700 nm goes in 5 times, but with some remainder. So we need 7 times something:

λ = 3952nm / 7 = 565 nm

Yes?