Solving Thin Film Problem: Find Longest Wavelength Transmitted to Diver

[idkgirl]

Homework Statement

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?

Homework 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.

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.

 

[ehild]

Homework Statement

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 spectrometer. What is the longest wavelength lambda_water of the light in water that is transmitted most easily to the diver?

Homework 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.

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.

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