# Thin film problem

1. Feb 12, 2013

### idkgirl

1. The problem statement, all variables and given/known data

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 {\rm nm} (in air). The index of refraction of water is 1.33

Now assume that the oil had a thickness of 200 \rm nm and an index of refraction of 1.5. A diver swimming underneath the oil slick is looking at the same spot as the scientist with the spectromenter. What is the longest wavelength lambda_water of the light in water that is transmitted most easily to the diver?

2. Relevant equations

2t = (m+1/2)(λ/n) or 2t = m(λ/n) and of course, these depends on whether you want constructive or destructive. I think I want destructive because essentially, I want to know what wavelength I would see reflected. I think I have one phase change, so I would need the second equation more... I think.

3. The attempt at a solution

the only math I have done is this: 2*200 nm * 1.33

I use m = 1 since that should give you the largest wavelength (I hope). ...It's not getting me the right answer.

2. Feb 13, 2013

### ehild

You are right, the wavelength of the light which is not reflected, so transmits easiest into the water, is λ=2t n(layer). That is the wavelength in vacuum. The refractive index of the oil layer is n(layer)=1.5.

The problem asks the wavelength in water. How does the wavelength depend on the refractive index of the medium where the light travels?

ehild