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enter image description here

I've read several answers on here to similar questions, and I've also looked at several different picture interpretations to no avail. I can't wrap my head around it. I understand that under the assumption of L >> d, both rays from the slits are approximately parallel, but how are the two angles of $\theta$ equivalent? I'm assuming by alternate interior angles somehow, but I can't figure out how. Can someone draw it out for me or something? I'm at a loss.

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  • $\begingroup$ The angles of the two photon trajectories are obviously different. $\endgroup$ Oct 15, 2017 at 16:30

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If you refer to the yellow-shaded triangle, yes, you're on the right path: it is purely geometric. Excuse me I'm not going to work much more than a cheap paint picture ^^

Steps:

  1. (Green) If the angle $\theta$ is that one, you obviously have 90 degrees minus $\theta$ until the slit-wall.
  2. (Blue) We are supposing that all rays are parallel.
  3. (Pink) We draw a perpendicular to the rays.
  4. (Red) Now focus on the upper triangle. If one angle is 90º and the other is 90º-$\theta$, the remainging one is neccesarily $\theta$ as well.

I hope you can see it now.

enter image description here

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  • $\begingroup$ Ah, I want to yell. I'm embarrassed that I didn't see this. Thanks. Great answer. $\endgroup$
    – Shocked
    Oct 16, 2017 at 0:57
  • $\begingroup$ Don't worry. Things are always obvious AFTER the explanation, but not before. Even the simpler things can be difficult if nobody explains. Check that the yellow triangle can also be seen as a rotation of 90 degree of the blue one. $\endgroup$
    – FGSUZ
    Oct 16, 2017 at 13:08

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