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I have an intuition problem when imagining the interference of two waves constructively and destructively. Here is a picture of the experience and the waves (taken from a KhanAcademy video):

Experiment

So how come there is constructive interference exactly in the middle, even though the waves don't add up "peak" to "peak" (isn't it just a bit beside the peek?)

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If the slits are in-phase sources, then the waves from them will arrive in phase at all points equidistant from the sources (that is "exactly in the middle"), as well as at certain other points (given by the 'path difference' rules). Where waves arrive in phase, they interfere constructively. One such place would be where two peaks intersect on the pattern, but don't forget that the waves are progressing, and that all the points through which the intersecting peaks pass marks a line of constructive interference. Try to think about in phase points rather than peak-on-peak.

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    $\begingroup$ I sort of get it now. So the lines are the peaks of the waves, thus the points formed in between two lines would be a valley. If a point between two waves was to interfere with a peek, the result would yield 0, which is why there is no light I think. $\endgroup$ – Imagine Dragons Aug 18 '17 at 21:35
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The points on the diagram where there are intersections ( x ) are where constructive interference occurs. You can then draw a line through X's going from left to right to complete the location of constructive interference. You'll see that one of these lines goes straight across from left to right exactly half way between the two slits. The X's indicate where the peaks add up. The other points in between ( on the line ) are still adding constructively but the phase of the waves are different. So, where you have phase=pi/4 on one wave will match the same phase at the same location for the other wave. Half way in between the lines that you draw through the X's are the destructive interference patterns.

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