In the double slit experiment shown in the figure, the slit spacing is d and the

Question

In the double slit experiment shown in the figure, the slit spacing is d and the distance from the slits to the screen is L . A piece of transparent plastic , with a thickness t and an index of refraction n , is placed over the upper slit. As a result, the central maximum ( the m=0 peak) of the interference pattern moves up by a distance y’ ; derive an expression for y’ in term of n, t, L and d. Please don't just give me random equations without explaining where they are coming from/why we are using them.

Explanation / Answer

here

the phase difference for going through plastic sheet

phase difference = 2 * pie * (t /lambda) * ( n - 11)

then

the path length difference

delta r = phase difference * ( lambda / (2*pie))

put value of phase difference

delta r = 2 * pie( t/lambda) * (n -1 ) * (lambda / (2*pie))

delta r = t * (n-1)

afterthis the angle of centeral maxima

tan(theta) = delta r / d = y' / L

y' / L = t * (n-1) / d

y' = t * (n-1) * L / d

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