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I have a question about the Michelson Interferometer with spherical waves: I know that the pattern produced by this kind of waves is a pattern of concentric circles. But what I'm not sure is how the pattern changes when I move one mirror. I believe that If I move the mirror away from the beam spliter, the circles in the pattern will move from the center of the screen to the sides of the screen, i.e. the radius will increase. Am I right?

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You should have a look at this question: Do interference rings disappear in an interferometer if the path lengths are identical? It somewhat addresses your question.

As for how the rings will change as you lengthen one of the arms; this could depend on a number of things. If your Michelson is symmetric in all respects, except that one of the arms is longer than the other, then the rings will grow (increase in radius) as you head in the direction of the arms being the same length (towards symmetry). Eventually, when you reach the point where the arms have the same length, the rings will disappear all together as described in the question linked above.

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