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wide laser beam - -> \ - - - leg 1 - - > / - - - > IYour layout uses two half mirror traversals for leg 1 and none for leg 2.
I ^ I
I I screen
I I
I I
\ - - - leg 2 - - > /
Upper slashed lines (in leg 1) represent semitransparent mirrors, lower slashed lines represent ordinary mirrors. Suppose a microscopic slide, partially covered with a transparent thin film, is introduced into leg 1. My expectation is that interference of two beams (observed on the screen), traversing the slide and not traversing the slide, will result in phase contrast. That demonstration (turning an invisible "phase image" into a visible "amplitude image," would be easier to understand than what happens in a phase microscope. Is there anything thing wrong with this idea?