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    Re: sextant precision.
    From: George Huxtable
    Date: 2005 Jun 22, 10:10 +0100

    Bill wrote, about the possible effect of offsetting incoming light rays to
    a sextant, with direction unaltered-
    >I have thought it (and sketched it) and am not clear I am wrong.  Let's use
    >a star, and assume its rays to be parallel for all practical purposes.  We
    >make our horizon and index mirrors parallel.
    Yes, OK.
    >This sets equal angles between
    >the scope line of sight/horizon mirror and horizon mirror/a point on the
    >index mirror (hopefully at the axis).  The reflected and glass images
    >coincide. If we were to offset the parallel ray striking the index mirror
    >(or change the geometry of the sextant by raising the index-mirror axis
    >vertically) the images would no longer coincide.
    That's where your mind-picture is wrong, Bill. Forget about "a point on the
    index mirror (hopefully at the axis)". For a plane mirror, one point is as
    good as another; none has any special significance. If you unshipped the
    index mirror from its mountings, you could move it about IN ITS PLANE, and
    as long as it could still reflect some starlight down to the horizon
    mirror, the star images would still coincide. I think that's probably obvious.
    Now shift the index mirror away from the horizon mirror in a direction
    PERPENDICULAR TO ITS PLANE, moving it upwards and backwards so it can still
    reflect some incoming starlight into the index mirror. As long as the index
    mirror is kept exactly parallel with the horizon mirror, you could shift it
    is far as you wanted, many feet away if you wish, and the two star images
    will remain coincident. It's because the starlight is coming from infinity,
    and is all exactly parallel. That would not be the case if the light was
    diverging from a nearby object; indeed, that's how a rangefinder works.
    >My contention is that a optically perfect shade with faces parallel will
    >still offset the ray if not perfectly perpendicular to the ray path.
    Yes, it will; we agree about that offset.
    >are probably correct that the offset is negligible in practice, but
    >nonetheless does exist.
    No, I didn't argue that at all. The offset can be as big as you like.
    However big the parallel offset is, as long as the DIRECTION of the light
    is unchanged, the star images seen in the telescope will still exactly
    If Bill (or anyone else) remains unhappy about that argument, I hope he
    will express his concerns, and we can thrash it out between us a bit
    further. Perhaps he isn't the only listmember to be troubled by these
    concepts, so it may be worthwhile clearing the matter up in a way that
    makes everyone happy about it.
    On a related topic, Renee Mattie wrote-
    I attempted the following experiment with my Freiberger:
    * I set my sextant near 0, took it into the closet, and laid it on its back
    on the carpet.
    * I shone a laser pointer through the scope and observed the spot on the
       Actually, I observed two half-spots unless I made a suitable index
       But I extinguished the horizon half-spot with the entire stack of shades
    so it would
       not distract me from the index-mirror half-spot.
    * When I swung the densest index-mirror shade in front of the mirror, it
    extinguished the half-spot.
    * Therefore, I could not observe any deflection of the spot caused by the
    darkest shade,
    did not repeat the experiment on a more stable platform, and did not attempt
    to observe
    deflection caused by the other 3 shades.
    The laser pointer is 7 or 10 years old, and there is no way to replace the
    I wonder if a brand new one would be bright enough to shine through even the
    darkest shade?
    There's an ingenious example of lateral thinking!
    I haven't come across a laser being employed in sextant alignment before,
    but it may indeed have its uses. Renee is using what I vaguely remember as
    being called the "reciprocity principle" for light. This is a fancy way of
    saying that if a light-ray takes a certain path through an optical system,
    if you send light back through the system in exactly the opposie direction,
    it will exactly retrace the same path. Perhaps that's so obvious as to go
    without saying.
    To get the light-beams to converge at a spot so close as the facing wall of
    Renee's closet would require quite a lot of "index correction": and
    "off-the arc", if I've assessed it right. Unless Renee has a VERY big closet...
    Renee's conclusion doesn't surprise me; that the darkest shade is so very,
    very, dark that not enough of the laser light is transmitted as to be
    visible. Perhaps, if that shade has a blue tint, like mine does, its
    transmission of the red light from the laser is even less.
    Contact George at george@huxtable.u-net.com ,or by phone +44 1865 820222,
    or from within UK 01865 820222.
    Or by post- George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13
    5HX, UK.

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