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How would the expression for the intensity distribution produced by a double slit on a screen change if a focusing lens of focal length $f$ were placed a distance $f$ in front of the screen?

The general intensity of the double slit experiment is: $$I=I_0\left(\cos\left(\frac{\pi ax}{\lambda D}\right)\right)^2.$$

Will the light just all pass through the focus, creating one bright spot on the screen and nothing else?

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  • $\begingroup$ I have realised that my original assumption is incorrect-- the light entering the lens will not be parallel, so will not pass through the focus $\endgroup$
    – mp12853
    Commented Aug 28, 2021 at 16:06
  • $\begingroup$ If you use the lens to image the double slit on the screen, you'll find that each photon will land on the screen at one of two locations, corresponding to each of the two imaged slits. It will look as if each photon definitely passed through just one slit, in seeming contradiction to the scenario where the lens is removed. $\endgroup$
    – Ken Wharton
    Commented Sep 6, 2023 at 15:32
  • $\begingroup$ When you place a lens after the slits and get a focused image of the two slits on the screen, it is a classic case of losing the interference pattern due to potentially gaining 'which way' information. $\endgroup$
    – KDP
    Commented May 7 at 23:59

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The formula assumes that parallel rays from the two slits meet at a point on the screen. Unless the distance to the screen is large relative to the slit width, the screen should be at the focal point of a converging lens.

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  • $\begingroup$ I am not sure I understand what you mean. The formula I included is for the general intensity distribution produced by a double slit experiment (which includes the assumption that the distance to the screen is large relative to the slit width). (I have edited the question to try and make this more clear) $\endgroup$
    – mp12853
    Commented Aug 28, 2021 at 15:07
  • $\begingroup$ Using a lens after the slits lets you bring the screen closer. Using a lens before the slits lets you bring a line source closer. $\endgroup$
    – R.W. Bird
    Commented Aug 28, 2021 at 17:50
  • $\begingroup$ If I leave the screen where it is, will the interference pattern just get more spread out then? $\endgroup$
    – mp12853
    Commented Aug 28, 2021 at 17:56
  • $\begingroup$ If the screen is not at the focal point of the lens, the image will go out of focus. $\endgroup$
    – R.W. Bird
    Commented Aug 28, 2021 at 18:05

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