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    Re: Perpendicularity and other qstns.
    From: Frank Reed CT
    Date: 2004 Oct 13, 02:05 EDT
    Alex, try this:
    Get some paper and tape it to your floor (a modern floor that you trust to be flat) in a rough circular arc with a radius of, say, three feet. Next mark an exact center for this circle. Using a tape measure or just a stiff wire of the right length, draw a circular arc on the sheets of paper with about 120 degrees extension to it (I bet you can guess where I'm going by now...!). Now take a mirror off your wall (or "borrow" one from your neighbor). A mirror without a frame is best but not essential. And be sure it's a nice big mirror with a good flat surface --no 'fun house' mirrors allowed. It shouldn't be too hard to find one that's two feet tall and a foot and a half wide, a typical 'portrait' wall mirror. Find a way to support this mirror so that it is vertical with its face directly above the center of the circle that you previously marked. Orient the mirror so that you can see the far end of the circular arc in the mirror and alongside it a direct view of the other end of the arc. Would you agree that this is 100% analogous to the standard sextant test for mirror perpendicularity? Carefully adjust the inclination of the mirror until the two arcs, direct and reflected make one seamless arc in your field of view. At this point you might want to check the tilt of the mirror with a level to verify that it is indeed perpendicular to the floor, but this is not essential (you could use a washer tied to a string hanging off the back of the mirror). Now, because the mirror is large compared to the radius of the circular arc, you can view the reflected and direct images over a VERY wide range of angles with respect to the horizontal from almost zero to almost 45 degrees.

    I just spent about fifteen minutes in my kitchen doing this myself to see if there was ANY effect at large angles. From what I saw, there is none. When I was right down close to the floor, the reflected and direct arc were exactly aligned. When I was standing upright and looking down at almost a 45 degree angle, the two arcs were still aligned PERFECTLY. Next, I moved the mirror one inch off the center of the circle. Displaced in that way, I saw an effect very similar to the one that you described; the alignment of the arcs changed with viewing angle. So once again, I think Herbert Prinz was correct. This phenomenon exists only when the mirror is displaced significantly from the center of the arc (how much constitutes "significantly" would be another question). I would not have guessed that a sextant would work if the mirror was displaced but upon further "reflection" (ouch), it is clear that the exact placement of the mirror at the center of the arc is not at all necessary to the instrument's operation. It is simply a historical fact that most sextants were constructed in that fashion.

    Please do not trust my empirical results. Try the experiment yourself.

    Oh and don't break any mirrors!

    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
       
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