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# Does a pentaprism REALLY maintain beam perpendicularity regardless of orientation?

## Does a pentaprism REALLY maintain beam perpendicularity regardless of orientation?

(OP)
I have found lots of references that claim that a pentaprism always bends incoming beams 90 degrees, regardless of beam orientation relative to the entry face ("within small angles").

Is this really true? Or is it one of those Physics 101 lies that are convenient approximations for people who don't really care?

I have worked through this "by hand" using Solidworks to sketch out the beam path in 2D and in 3D.

In 2D, everything works just fine. Any beam that enters the prism will exit at 90 degrees. Small angle seems to be defined as "beam path stays inside the glass."

In 3D, where the beam enters out-of-plane, things don't go so well. Maybe it's my 3D sketching skills? I find that as the beam deviates from in-plane, the entry and exit beams become more and more skewed (no surprise) but also at less and less of a right angle (further from 90 degrees). This part is a surprise. I do find that the error is small, as long as the entering beam is within a few degrees of true. But a small error is still an error. A beam that is out-of-true by 0.05 degrees will move 0.105" at 120". Not a big deal? It is if you are trying to align some linear bearings over that distance!

NOTE: I measured beam perpendicularity in SolidWorks by drawing a line segment perpendicular to entering and exiting beams, creating a sketch plane normal to that line (The resulting plane should be parallel to both entering and exit lines), projecting both beams onto it, and measuring the resulting angle. I think this is an accurate way to measure "perpendicularity" of two skew lines.

Can someone smart either confirm this non-ideal behavior or tell me what I'm missing?

Thanks!

William.

### RE: Does a pentaprism REALLY maintain beam perpendicularity regardless of orientation?

I think the assertion that the pentaprism always bends the beam by 90 degrees is only true within a plane parallel to its major plane of symmetry and confined to the locus of the prism, e.g. in a 2D model, and is further subject to manufacturing errors. I.e. all bets are off for skew rays.

Mike Halloran
Pembroke Pines, FL, USA

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