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Can it be proved that there would be no change in the "fringe width" when the main illuminated slit(s) is shifted to a position, which makes an angle of $\Theta$ with the original position of the source slit?

My try - I first found out the fringe width in a normal double slit where the position of the source slit is unchanged. However, after that, As I tried for the new position of the slit, I got stuck and couldn't equate the two values of fringe width.

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enter image description here Hope you understand by the above explanation . I had a sample question also. enter image description here

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The fringe pattern or spacings will not change. As long as D and d and the wavelength stay the same the position or angle of the light source will not matter. The only thing that may change is the location of the maximum bright spot on the detection screen but the pattern will remain the same. I cover this on page 5 and 6 of my paper "single edge certainty" at billalsept.com

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  • $\begingroup$ I know that. I am asking, how can we prove it? $\endgroup$
    – Sid
    Nov 16, 2016 at 10:54
  • $\begingroup$ You can prove it by experiment or by derivation as I did in the paper. $\endgroup$
    – Bill Alsept
    Nov 16, 2016 at 15:53

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