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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 [Broken]

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.

## Homework Statement

## Homework Equations

## The Attempt at a Solution

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