I don't think you can guarantee that the angle that a light ray enters a fiber
is the angle at which it leaves the fiber, since that would mean an even number
of reflections down the fiber.  It there were an odd number of reflections, it
would exit on the other side of the axis of the fiber.  I think that rays
entering at different angles would have a different number of reflections.
Imagine two parallel mirrors and a ray bouncing between them from one end to
the other.  Since we are installing some fiber cables here at work, I'm trying
to find some scraps.

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