# Refractive indices

1. Nov 14, 2007

A scientist notices that an oil slick floating on water when viewed from above has many different rainbow colors reflecting off the surface. She aims a spectrometer at a particular spot and measures the wavelength to be 750 nm (in air). The index of refraction of water is 1.33.

The index of refraction of the oil is 1.20. What is the minimum thickness t of the oil slick at that spot?
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All right, I know that light reflects off the two different surfaces of the film (air-oil interface and oil-air interface).
I also know that this phase difference one talks about is between two waves and when the difference is a full wavelength then the waves interfere constructively and if the difference is half a wavelength then the waves interfere destructively....
The light that that reflects off the oil-water interface has to pass through the oil slick where it will have a different wavelength. & The total extra distance it travels is twice the thickness of the slick.

How do I put this info together to solve the prob???????

So I found this equation 2 * n (refractive index of oil) * d (thickness of oil) cos beta= (m-0.5) lambda where Cos beta has a maximum value of 1 so you can get the minimum value of 'd'. But when I solve fore d, I don't get the right answer...

I really want to understand this, so please tell me if I am approaching this wrong.