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The Wikipedia page for the double-slit wave interference experiment states that the path difference between waves diffracting from the two slits is equal to:

$$ \Delta l=d\sin \theta $$

where $d$ is the distance between the two slits and $\theta$ is the angle defined in the diagram on the same page (between the line bisecting the two slits and the point of interference).

Does anyone know how this path difference is derived? It seems like it should be a fairly simple geometric relationship, but I can't figure it out.

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    $\begingroup$ This is all over the internet, and in almost every physics textbook in the world. Did you try googling it? $\endgroup$
    – hft
    Commented Apr 25, 2015 at 21:17
  • $\begingroup$ @hft: Fair enough - I probably could have searched a bit harder first. $\endgroup$
    – Time4Tea
    Commented Apr 26, 2015 at 1:48

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This diagram would help. You need to approximate the two longer sides of the trangle to be parallel to obtain $\varDelta l = d \sin \theta$.

enter image description here

Source: http://www.wikipremed.com/01physicscards.php?card=876

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