Oil in puddle of water?

Question

A thin film of oil (n = 1.52 is spread over a puddle of water (n = 1.33). In a region where the film looks red from directly above (lambda = 626 nm), what is the minimum possible thickness of the film?

Answer 1

What you are looking at is, essentially, a 1-layer dielectric mirror.

What you want to find is the thickness such that when the light goes to the bottom of the oil and reflects back, it will be in phase with the light reflected from the top of the oil layer.

But the light reflected from the top of the oil undergoes a 180 degree phase change, while the light going through the oil does not:

http://hyperphysics.phy-astr.gsu.edu/hba...

So the thickness of the oil must be such as to cause a 180 degree phase change when the light traverses it twice (once down, once up). That means twice the thickness must equal N + 1/2 wavelength in oil, for any integer N. The minimum is when N = 0.

wavelength = velocity/frequency

http://en.wikipedia.org/wiki/Wavelength

Since the frequency (color) of the light does not change, the change in velocity means a change in wavelength. So, all you have to do is compute the length of a quarter wavelength in oil.

And you can check it with:

http://hyperphysics.phy-astr.gsu.edu/hba...