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Const@ntine

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## Homework Statement

Two glass plaques of length 10.0 cm osculate, on one end, and are separated by a wire of diameter d = 0.0500 mm on the other. Light with two wavelengths (400 nm & 600 nm) falls on one of them, and we can see it gets reflected. At which distance from the point of contact does the next dark fringe form?

## Homework Equations

2nt = mλ

2nt = (m+1/2)λ

dsinθ

_{light}= mλ

dsinθ

_{dark}= (m+1/2)λ

## The Attempt at a Solution

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My problem here is that I can't really understand the significance of the two wavelengths, how to use that info and generally how to proceed. My book has a small paragraph on TFI, and only explains the basic stuff (the above formulas for a single instance and that's it). Anyway, I figured:

>d = t : So d, the diameter, plays the role of the thin film's thickness.

>The thin film is the air, and the glass plaques have the same n

_{g}, which while bigger than n = 1.00 of the air, is still the same from above and bellow the thin film/air, so I don't have to inverse the two formulas.

>So, 2nt = mλ for destructive confluence, and 2nt = (m+1/2)λ for amplified confluence.

Now, the only thing I came up with was: Take the first formula (for destruction) and try it with both λs, to see which one gives me an integer m. 400 gives me n = 250, whereas 600 gives me 166.6666...7. So, I figured I'd continue with the first wavelength. Then I went back to the chapter about light and dark fringes, and looked at the formulas.

Now it gets murky and I'm just throwing stuff at the wall to see what will stick, but my plan was to put in the data in the "dark fringe" equation, find the angle, then put it in tanθ = y/L and find y. But that didn't work out. So I need some help here.

Any help is appreciated!