## GRE0177 #69

ma_
Posts: 1
Joined: Fri Sep 21, 2007 6:22 am

### GRE0177 #69

I'm havn't studied optics in a while so i'm having some trouble with this problem. Can anyone offer some help?

butsurigakusha
Posts: 293
Joined: Sun Oct 07, 2007 8:05 pm
The formula is 2*n*t=m*lambda, where n is the index of refraction for the thin film and t is the thickness of the film. With thin film interference problems, you have to be careful, because depending on the setup, this formula may give complete reflection or no reflection. I was never really into memorizing stuff, so what I would recommend is to understand the theory behind the formula, and then you can always figure out which one to use in a given situation.

When light is incident on a thin film, some of the light will reflect and some will transmit. Then, when the transmitted light reaches the other side of the film, the same happens, with some of the light reflecting. If the light that reflects off the second surface is in phase with the light off the first surface, you will get a bright spot. That's where the 2*n*t =m * lambda comes from, since the light travels twice the thickness of the film. But, something you also have to take into account is that there is always a 180 degree phase shift for light that reflects off of a higher index material. That changes the formula to 2*n*t=(m+1/2)*lambda. In this problem, however, the light is going from air to the oil, which results in phase shift, and then it goes from oil to glass, which also results in a phase shift. Since both reflections have phase shifts, the effect cancels, and you can just pretend that there was no phase shift.