A problem involving dark fringes & light wave & interference.

erinec

1. The problem statement, all variables and given/known data
Two pieces of optically flat glass (n=1.5) touch at one edge and are separated by a thin stretched fibre at the opposite edge. Light of wavelength 500nm is shone from above and 100 dark fringes are counted. The air between the glass is now replaced by water (n=1.33). How many dark fringes are now observed?

a) 133
b) 75
c) 150
d) 100
e) 67


2. Relevant equations
2nt = (m+0.5)(lambda)
.. I think?



3. The attempt at a solution
I assumed that since the index of refraction for both water AND air are smaller than the index of refraction for glass, it does not make a difference. So I chose d)100. However, the answer is supposed to be a) 133.

alphysicist

Hi erinec,

No, I do not believe this is the correct equation. There is one phase reversal here, so the other equation will give the destructive interference conditions.

In this problem the film is not the glass, it is whatever is between the glass. So when you change from air to water, you change the n value in the destructive interference equation.

erinec

Hi alphysicist,

Thanks a lot for your insight.

Would you be so kind enough to explain why the film is whatever is between the glass and not the glass?

I appreciate your help very much.

alphysicist

When we talk abou a "thin film" here we mean a material whose parallel boundaries are close enough so that light reflecting off the boundaries can interfere.

Here you have a thick piece of glass on the bottom, a thick piece of glass on top, and a very thin space that is either filled with air or water. So the air or water will be the thin film.

(The space has a triangular outline, since the glass pieces touch at one end and are separated by only a wire at the other end. But it's a very thin triangle! and it is the triangular shape that makes you have a series of lines--because the thickness of the film changes as you move from one end of the space to the other.)

erinec

I see.
So if the gap is too large, it wont work right? (Just making sure.)

Thank you!!