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I was wondering that how position of source of light affects YDSE experiment? I know that path Difference of light after the slits is the reason for YDSE interference pattern observed, but how path difference from source to slits affect YDSE?

PATH DIFFERENCE BEFORE SLITS CAN BE CREATED BY TILTING THE SOURCE OR USING LENS IN HALF OF THE WAVE FROM SOURCE.

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This is the diagram we typically use for the Young's slits:

Young's slits

The extra path length in the top ray is the region indicated by the arrow, and it has a length $d\sin\theta$. For constructive interference we require this length to be a whole number of wavelengths, $n\lambda$, and that gives us the equation for the maxima:

$$ n\lambda = d\sin\theta $$

You are asking what happens if we angle the input rays, and in that case we get something like this:

Young's slits

Now there is an additional difference in the path length equal to $d\sin\phi$, where $\phi$ is the angle of the input rays. So the position of the maxima changes to:

$$ n\lambda = d\sin\phi + d\sin\theta $$

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