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    Re: Sextant scopes and an old-bold empiricist
    From: George Huxtable
    Date: 2006 May 2, 11:23 +0100

    Bill wrte, about optics of sextant terlescopes, and measuring magnifiucation-
    |...and like the "tracing paper" suggestion
    | for determining power.  It only just occurred to that the diameter of the
    | exit pupil will be the diameter of the objective lens /power. I am a bit
    | fuzzy on how far to place the tracing paper from the ocular lens.  My best
    | guess is to let the built in eye relief serve as a guide.
    Close up as possible, really. But it shouldn't matter much. With a telescope 
    adjusted so that the image of a distant object is clear
    to the eye, even an eye that normally uses specs, the light that leaves the 
    telescope isn't that far from parallel. The size of the
    disc of light that leaves the eyepiece won't be growing or shrinking fast as you move further back.
    Bill goes on to comment-
    | Field glasses (long binoculars--no Porro or roof prisms) seem
    | to have a third (center) lens set instead of a prism pair to keep the image
    | from being inverted.
    Yes, they have an extra stage, at the input to they eyepiece, which performs 
    an extra inversion, so as to put the picture the right
    way up again.Usually, four lenses are used for that combination of erector and 
    eyepiece, and with the object glass, that makes five.
    The significant price to be paid is the considerable extra length of the 
    combination. For that reason, I doubt if such scopes were
    used for sextants, but could be wrong. The length would put the sextant out of 
    arm's reach, or at least, so far away that the
    leverage of its weight would be too great for the human arm to support. 
    Instead, navigators got used to the awkwardness of an
    inversion. The prismatic construction was a breakthrough. The prisms provided 
    the erection, and allowed for further shortening of an
    astronomical telescope by folding of the light-path, at the expense of some extra weight of glassware.
    Bill had asked, in his original message-
    | 4. Does the f-ratio (focal length over objective lens diameter) hold up for
    | prism optics?
    and I answered-
    "I'm not sure what question Bill is asking here. Yes, the objective lens 
    itself has a certain f-number, but not a telescope as a
    whole, as I see it. That's because the telescope does not have a focal length, 
    as such. It takes in parallel light and puts out
    parallel (or very nearly parallel) light. So the notion of f-number doesn't 
    fit with "prism optics" in the way Bill implies.
    Is Bill asking about the effect of the prisms on the brightness of the 
    resulting image, compared with an equivalent inverting
    telescope? Yes, the prisms must give rise to some light-loss, as any glass 
    element will, due to surface reflection and some slight
    absorption within the glass. But no more than that; no reduction due to geometry or optical differences."
    Bill now writes-
    | I am sorry if not clear.  In a camera lens objective diameter related to
    | focal length determines f-number (a "Reader's Digest" version of our
    | exchange on theoretical f-number vs t-number for a lens).  As I read it (and
    | I am on very shaky rope/line here, hence my desire to tight-rope walk with
    | the list as a net) a telescope's objective lens has both an aperture
    | (diameter) and a focal length.  How "nearly parallel" the rays are is
    | determined by the objective lens focal length.
    Yes; as I was trying to say above, the relevant focal length and diameter, and 
    the f-number (which provides information about the
    light-gathering efficiency), apply to the telescope's objective lens, not to 
    the optics of whatever follows the formation the first
    image, such as eyepiece, erector, prisms. Those components will, necessarily, 
    lose some of the light; the less they lose, the
    better. One has to assume that the diameters of those components, (and any 
    diaphragms in the light-path) are sufficient that they do
    not intercept and obscure any of the wanted light that has been gathered by 
    the objective. But some light will always be lost
    through reflection at glass surfaces, and a bit more by absorption in passing through the glasses.
    Take all the above with a pinch of salt, bearing in mind that I am in no way a specialist in optics.
    If Bill would like to do a bit of reading, there's a nice little 1960 Dover 
    paperback, "Optics and Optical Instruments", by B K
    Johnson, a reprint of his 1947 "Practical Optics", which has supplied much of 
    my own information. But bear its date in mind; it will
    tell nothing about the considerable postwar developments of aspheric surfaces, 
    computer lens design, exotic optical materials, etc,
    that have transformed the technology, mainly the result of Japanese ingenuity.
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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