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This page claims that the Michelson interferometer below enter image description here

is equivalent to the optical system bellow. enter image description here

How can it be? Where did the beam splitter go? And in the second system we restrict the incident beam of light from the source to be making the same angle $\theta$ with respect to the normal of both mirrors, this was certainly not the case in the Michelson interferometer (the beam of light striking mirror 1 could for example be at $\alpha$, while the one striking mirror 2 could be at $\beta$), so why add this restriction?

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The two are equivalent because if you put your eye at the screen and looked back into the system, you would see the point sources at the same positions in both setups. Just trace the beams back to prove this to yourself.

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  • $\begingroup$ I respectfully disagree, the point source is in front of the screen in the second diagram, whereas it is at a $45°$ with respect to screen in the second. I've been contemplating the second figure for a while and still can't see why restricting the ray that strikes mirror M1 and the one that strikes mirror M2 to the same angle is a legitimate move from the first to the second diagram. Shouldn't we have something more general, like this, for instance. $\endgroup$
    – Hilbert
    Feb 7, 2020 at 19:41
  • $\begingroup$ If you consider the beamsplitter to be a mirror for the portion of the light that it reflects, you will see that it places the images of the point sources together at a position directly normal to the screen, at a distance of twice the width of the interferometer. That is, at a distance of S-M1-BS-screen, which equals the distance of S-BS-M2-screen. All the rays come to the screen as if emitted from points at that distance along a line normal to the screen. $\endgroup$
    – S. McGrew
    Feb 7, 2020 at 19:50
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    $\begingroup$ In the "more general" diagram, the source point is simply moved to one side. Do the same in the Michaelson interferometer, and the results are the same as in the "more general" diagram. The only meaningful difference is that the beamsplitter serves to fold the beam paths, so one mirror doesn't need to be directly in front of the other. BTW, in my previous comment I left out the fact that the two paths differ in length by some amount: 2d in "more general" and "2x translate" in the Michaelson interferometer. $\endgroup$
    – S. McGrew
    Feb 7, 2020 at 19:56
  • $\begingroup$ Another way to reply to the objection in your first comment is to point out that if a piece of black cardboard were placed diagonally from the upper left corner of the Michaelson diagram, to somewhere near the beamsplitter, it would not block the rays that form the interference pattern, nor would it affect what you would see if you looked from the screen upstream into the light. $\endgroup$
    – S. McGrew
    Feb 7, 2020 at 20:10

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