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!
Best Answer
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
sincand acosfunction where slit width is 1/6th of the spacing: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.