I want to ask a question about double slit interference and the pattern that it produces on a screen (for example in Young's Experiment with a laser beam). I understand the reason that you see a series of light and dark spots - constructive and deconstructive interference due to different path differences. However, I do not understand why the central maximum is a lot brighter than all the subsidiary maxima. The intensity is higher in the centre, but why? Surely if complete constructive interference is occuring in all of these spots then the combined amplitudes will be the same and hence the brightness/intensity will also be the same? Is it to do with the number of rays that converge at each point? or the angle at which they hit?

Many thanks in advance!

  • $\begingroup$ Can't it be that you make a confusion between the diffraction pattern of the double slit, and single slit? In the former I didn't see a specially enhanced central fringe, but in the latter yes, because the pattern goes in principle like $sinc^2(k\theta)$, function that has a very high central maximum and double in width that the subsidiary maxima. $\endgroup$ – Sofia Mar 15 '15 at 22:53
  • $\begingroup$ In a single slit experiment the central maximum is definitely more enhanced than than the subsidiary ones. But from diagrams I have seen the same thing occurs in a double slit experiment. The rate of reduction of intensity is definitely lower, but as far as I'm aware it still exists $\endgroup$ – bnosnehpets Mar 15 '15 at 22:58
  • $\begingroup$ here is a totally random picture of the pattern bit.ly/1NYiyts IMO it seems to depend on the particular photo taken on the day but this one seems even all the way across to me, as Sofia says $\endgroup$ – user74893 Mar 15 '15 at 23:23
  • $\begingroup$ @user75473 I looked at the pictures that you indicate. In pictures of double slit I didn't see a central maximum as in the single slit. $\endgroup$ – Sofia Mar 16 '15 at 1:15

The problem is that the dual slits are not infinitely narrow - the slit pattern is in fact the convolution of two infinitely narrow slits with a single wider slit. By the convolution theorem, the diffraction pattern, which is the Fourier Transform of the aperture function, is the product of the two Fourier transforms - so you see a series of equal intensity fringes modulates by a sinc pattern. How quickly the intensity falls off depends on the relative size of slit and spacing.

Here, for example, is the squared product of a sinc and a cos function where slit width is 1/6th of the spacing:

enter image description here

It is pretty obvious that you will get brighter fringes in the middle, and they will fall off quickly. Further out they may come back again - that would be a sure sign that you are looking at the sinc pattern of the individual slits.

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  • $\begingroup$ But the wide sinc pattern is not supposed to be double? I.e. for each slit one such broad pattern? Or, maybe, since the slit are close to one another, the two broad patterns superpose into one ever wider? $\endgroup$ – Sofia Mar 16 '15 at 2:07
  • $\begingroup$ @Sofia the final pattern is the product of a sinc and a cos function. The sinc acts as an envelope of the cos. $\endgroup$ – Floris Mar 16 '15 at 2:08
  • $\begingroup$ Yes, it seems to me that I saw such a formula $\endgroup$ – Sofia Mar 16 '15 at 2:09
  • $\begingroup$ See also universe-review.ca/I12-21-twoslits.jpg $\endgroup$ – Floris Mar 16 '15 at 2:22
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    $\begingroup$ Thanks for your answer. some of the physics you talk about is a bit beyond me at the moment, but I think I get the gist. The linked image really helps it make much more sense $\endgroup$ – bnosnehpets Mar 17 '15 at 18:27

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