Wedge interference - solving for 'separation of fringes' without lambda

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The discussion focuses on calculating the separation of dark fringes in an interference pattern created by plane glass plates held apart by a wire. The problem involves using filtered green mercury light and requires understanding the relationship between fringe separation and wavelength. Participants emphasize that the wavelength of the light is essential for determining fringe width, as it cannot be canceled out in the calculations. The equations provided relate to the geometry of the setup and the interference pattern. Ultimately, solving for the wavelength is necessary to proceed with the calculations effectively.
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Homework Statement


plane plates of glass are in contact along one side and held apart by a wire 0.05mm in diameter, parallel to the edge in contact and 20cm distant. using filtered green mercury light, directed normally on the air film between plates, interference fringes are seen. calculate the separation of dark fringes. how many fringes appear between the edge and the wire?


Homework Equations


t=x*theta=m*(lambda/2)
delta x = x*(lambda/(2*t))


The Attempt at a Solution


i've been using ratio and proportion here since theta will remain constant. however, i cannot get to cancel out lambda nor m. is it necessary to solve for the wavelength of 'filtered green mercury light' first, so everything else will be plug and chug?
 
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Yes. Without the wave length you cannot find the fring width.
 
Thread 'Correct statement about size of wire to produce larger extension'
The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...

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