Air Wedge radius of the wire Problem

1. Aug 17, 2008

Zukie91

The problem statement, all variables and given/known data
An air wedge is formed between two glass plates separated at one edge by a very fine wire. When the wedge is illuminated from above by 600 nm light, 30 dark fringes are observed. Calculate the radius of the wire.

The attempt at a solution
Wasn't really sure how to go about doing this, also don't have the answer, so i have no way of knowing if i am correct.
I think it has something to do with every time it goes light dark light, is one wavelength. not sure if that is relevant (or even correct) any help is appreciated.
Thanks

2. Aug 17, 2008

Kurdt

Staff Emeritus
For this particular problem, the fringes correspond to integral numbers of wavelengths. As you go along to the next fringe it represents the next integral number wavelength phase difference which corresponds to a change in thickness of the air gap of half a wavelength. Thus there is a relationship between the maximum thickness of the air gap (i.e. the wire) the wavelength and the number of fringes. Can you work out what that must be?

3. Aug 17, 2008

Zukie91

well, if there are 30 fringes, and each integral number wavelength phase dfference corresponds to a thickness of half a wavelength, would that mean at its thickest, the width is 15 wavelengths or 9000 nm?

4. Aug 18, 2008

Kurdt

Staff Emeritus
Yes that would be correct. But remember that the question asks for the radius of the wire.

5. Aug 18, 2008

Zukie91

right, what i have there is the diameter, so i would divide by two and the final answer would be 450 nm. Thanks

6. Aug 18, 2008

Kurdt

Staff Emeritus
Careful! You're on the correct track though.

7. Aug 18, 2008

Zukie91

whoops, typo, meant 4500 nm

8. Aug 18, 2008

Kurdt

Staff Emeritus
very good.