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    Re: Sextant optics
    From: George Huxtable
    Date: 2004 May 4, 21:09 +0100

    Ken Muldrew noted, among some other interesting stuff-
    >Magnification is given by the focal length of the objective divided
    >by the focal length of the eyepiece. In general, the greater the
    >magnification, the less the field of view, the lower the brightness
    >of the image, and the smaller the depth of field (the range of
    >distances that are in focus). Higher magnification must be
    >accompanied by a larger objective lens in order to allow the image to
    >be resolved, but this is unlikely to be an issue with the low
    >magnification used in a sextant.
    My knowledge about optics is limited to what I remember from an
    undergaduate course of 50-odd years ago, but perhaps I can add a bit to
    what Ken has said.
    His last sentence presumably refers to the diffraction limit on optical
    resolution, relating to the wavelength of light. As he says, for the low
    magnifications we are considering, that is not an issue: it's the acuity of
    the human eye (of about an arc-minute) that will dominate.
    But there are some optical "facts of life" that we are quite unable to
    alter, and govern the choice of magnification and size of objective.
    1. The pupil of the eye, when dark-adapted, opens up to about 8mm diameter
    at night. In daylight conditions depending on how bright or dull it is, the
    pupil diameter closes down to 2 to 4 mm. This varies very little, from one
    individual to another.
    2. Light emerges from the eyepiece of a telescope as a "pencil" of rays
    with a diameter exactly equal to the objective diameter divided by the
    magnification. Whatever sort of telescope you have, however you adjust it,
    there's nothing you can do (short of worsening it by stopping-down the
    objective) to alter that fact of life.
    3. Only that part of the exit pencil that can pass through the pupil is
    collected by the eye to form an image. Any excess light goes to waste.
    4. So in night conditions, the size of the objective that's needed for a X3
    telescope is 3x8mm or 24 mm. If the objective is any bigger, light from its
    outer parts misses the pupil and is wasted. And in daylight conditions,
    with a smaller pupil, there's no point in an objective bigger than 12mm or
    so. That's why telescopes and binoculars intended as "night glasses" have a
    bigger objective lens than others. The extra only becomes useful under dark
    conditions, when the pupil has dilated.
    5. If you want to collect more light at night, you can increase the size of
    the objective lens, but only if you increase the magnification accordingly,
    so that all the light is shrunk enough, as it leaves, to enter the pupil.
    If the magnification was 6x, your eye could collect all the light from a
    48mm objective. The trouble is that on a boat at sea, the motion can be
    such that this greater magnification becomes a serious disadvantage. Unless
    your telescope has that greater magnification, however, the larger
    objective would offer no advantage at all.
    6. Although this may not appear to be the case, a telescope does not
    increase the surface brightness of the objects you see in it, compared with
    what the naked eye sees: not even when viewed by a night-glass at night. It
    makes dim objects easier to see by making them bigger, not brighter. That
    does not apply, however, to a point-object such as a star, because when
    magnified a star remains a point-object: but a brighter one.
    7. No optical cleverness can change these ground-rules in any way. They are
    seldom explained, and little understood. It would be nice if someone could
    disprove what I have said, but I think that these are facts that we are
    stuck with.
    8. Of course, there are other ways in which light can be lost on its
    passage through a telescope: mainly due to reflection from optical
    surfaces. This can be minimised by suitable surface coating.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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