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Homework Statement
Plan plates of glass are in contact along one side and held apart by a wire 0.05 mm in diameter, parallel to the edge in contact and 20 cm distant. Using filtered green mercury light ([itex]λ = 546 nm[/itex]), directed normally on the air film between plates, interference fringes are seen. Calculate the separation of the dark fringes. How many dark fringes appear between the edge and the wire?
Homework Equations
The Attempt at a Solution
I'm trying to follow along with the solutions and I seem to get confused early on
http://imageshack.us/a/img844/8884/ix2m.png
I understand that
[itex]Δ = Δ_{p} + Δ_{r} = 2nt = (m + \frac{1}{2})λ[/itex]
Here [itex]n = 1[/itex] because of air and you use [itex]m + \frac{1}{2}[/itex] instead of just [itex]m[/itex] because you want a dark fringe. I believe the solution is using [itex]Δ_{r} = \frac{λ}{2}[/itex]. I'm however not really sure where this is coming from or why it's included. Apparently the geometrical path difference is [itex]\frac{λ}{2}[/itex] but I'm not really sure why.
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