Thin film appears red, thickness of this part?

[Cocoleia]

Homework Statement

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?

Homework Equations

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?

 

[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.

 

[kuruman]

So we get mlambda = 2d + lambda/2

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.

 

[Cocoleia]

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.

How would I find the correct wavelength?

 

[TSny]

How would I find the correct wavelength?

 

[Cocoleia]

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.
.

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

 

[TSny]

In your equation mλ_f = 2d +λ_f/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.