# Thin film appears red, thickness of this part?

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1. Nov 29, 2016

### Cocoleia

1. The problem statement, all variables and given/known data
A thin film of oil (n=1.5) is floating on top of water. When looking directly at this film, a large portion appears red (700nm). What is the thickness of the red part of the layer?

2. Relevant equations

3. The attempt at a solution
Since n for oil > n for air, there will be a phase shift of lambda/2
There will be no phase shift for the next reflection, but it travels 2x the thickness of the film (2d)
Since it appears red, i said it was constructive interference. So we get mlambda = 2d + lambda/2
If they asked for minimum i would set m=0 and use the 700nm to solve for d, but they don't specify. What should i do?

Last edited by a moderator: Nov 29, 2016
2. Nov 29, 2016

### TSny

You are right, there are different thicknesses (corresponding to different integer values of m) that would give constructive interference. I think they should have stated minimum thickness if that's what they wanted. The phrase "large portion of red" suggests that the thickness is very small, because with larger thicknesses the regions of interference maxima and minima tend to crowd together. But this still does not necessarily mean that you must pick the smallest thickness. So, I'm with you. The statement of the problem should have been clearer.

Note that if you choose m = 0 you will get a negative value for d. So, if you want the smallest thickness you would want to choose the smallest value of m for which you get a non-negative thickness.

Also, remember that lambda in the formula represents the wavelength of the light inside the film. So, you would not use 700 nm.

3. Nov 29, 2016

### kuruman

Not quite. You are forgetting that in the oil the wavelength is shorter than in air (or vacuum). Your expression does not take into account this fact.

4. Dec 1, 2016

### Cocoleia

How would I find the correct wavelength?

5. Dec 1, 2016

6. Dec 1, 2016

### Cocoleia

Can I choose m = 1 then? or will this no longer respect the conditions

7. Dec 2, 2016

### TSny

In your equation mλf = 2d +λf/2, any positive integer value of m would correspond to constructive interference. m = 1 seems like the most natural choice. It will give the smallest thickness.