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Prisms are frequently used to provide set of internal reflection mirrors that are at stable angles with respect to each other and immune to dirt accumulation spoiling reflectivity.

Image rotation characteristics of prisms are also possessed by mirrors.

Look in a mirror while holding a tablet of graph paper. Rotate the graphpaper and the reflection will rotate in the opposite direction. Said another way hold out your right hand the reflection will have its left hand out.

If you place two mirrors such that their normals form a right angle and view them along the bisector of those normals you have a mirror that doesn't switch right hands to left hands, the graphpaper and the reflection will rotate together.

I'm guessing even number of reflections means things should rotate same direction and odd number in opposite direction. That may be source of askewity?

Can't say I understand diagram of autocollimator. Should have three ports;. Source graticle, lens output/input to dut, and output view. Where is beamsplitter? There must be more details in prism/mirror assembly else why the angle in the beams going and coming from that structure. I think that would help in understanding dilema.

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