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is there any effect from index of refraction of the glass in
front of the silvered surface?

> Think of the mirror as a plane of clear glass perpendicular to the plane of
> the instrument. Rotate the glass on the axis of the instrument until the
> reflection of 120 degrees on the arc (as seen on the reflecting surface of the
> glass) coincides with 0 degrees seen through the glass. You'll find, of course,
> that the glass itself crosses the arc at 60 degrees, half way between 0 and 120.
> That's why the system of adjustment works.
>
> Now, keeping that plane of glass perpendicular to the frame of the
> instrument, move it a couple of inches away from the axis, toward the arc. The original
> system breaks down.

   

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