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    Re: Sextant scopes and an old-bold empiricist
    From: George Huxtable
    Date: 2006 Apr 14, 00:32 +0100

    Bill asked some questions about optics.
    I'll have a go at answering, though optics is not "my subject". So, take it for what it's worth.
    | I've been comparing a few "straight" lower-magnification (approx. 3X to 4X)
    | and higher-magnification (6X to 8X) prism sextant scopes .
    | I have a few questions:
    | 1. How many lens elements should I expect to find in 3X to 4X power
    | "straight" scopes?
    My plastic Ebbco sextant (3x) appears to have just two simple lenses in a 
    Galilean (opera-glass) configuration. That means it has a
    normal convex objective, and a concave (diverging, negative-power) eyepiece. 
    The advantage of that simple arrangement is that it
    results in a short telescope, and a non-inverting view. One disadvantage is 
    that there is no internal focus-point within the
    telescope, so there's no way to instal a crosswire, to centre your sightline on.
    | 2. How many lens elements should I expect to find in 6X-8X prism scopes.
    I do not know if makers use multi-element lenses to overcome chromatic 
    aberration. That would allow light of different colours to
    focus in the same way. It's how the more expensive refractor telescopes for 
    astronomy are made, with compound objectives and
    multi-element eyepieces. Somehow, I doubt if that would be thought necessary 
    for a sextant, but others may know better. If I'm
    right, then just two lenses, both convex.
    | 3. How many lens elements should I expect to find in a 6X inverting scope?
    | (I know Alex has the answer to this, as he has disassembled his SNO-T
    | inverting scope).
    The same as for a prism scope, I suggest. Optically, the two are the same, 
    except for the insertion of a prism-pair reflector which
    corrects the inversion, and shortens the system by simply folding the light path.
    | 4. Does the f-ratio (focal length over objective lens diameter) hold up for
    | prism optics?
    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..
    | Now the sticky wicket--determining magnification. Problem at hand, no lab,
    | no optical bench, no degree in optical engineering.  I need to take sextant
    | scopes with no specs (except diameter of objective lens, and determine their
    | respective magnifications.
    | All I can figure is to focus all the scopes with a given eye, solidly tripod
    | mount them, put shades (filters) in front of the objective lens to protect
    | the (glue?) mounting of lenses/prisms from the heat (noting an astronomy
    | caution that telescopes can take the heat, but binoculars cannot), and point
    | at a known object (sun?).
    | Then introduce a target (piece of white board) behind the exit pupil and
    | move them to bring the sun's projected image into sharp focus (like viewing
    | the sun through a telescope and projecting it onto a piece of paper/board).
    | Measure and compare the diameter of the projected circles to the sun's SD.
    | (Caveat here being that image size will change as the scopes focus--barrel
    | extension--is changed. Hence common focus. Much easier if the magnification
    | of one of the scopes is known as a reference.).
    I don't think that's the right way. A telescope is usually adjusted to take 
    in, and put out, parallel light, or nearly so. Correctly
    adjusted for an observer who doesn't need specs for distant vision, that would 
    be exactly true. Adjusted for someone who requires
    specs for distant vision, but wanted to use the telescope without wearing 
    those specs, then the light from the telescope eyepiece
    would be convergent or divergent, as appropriate, but only slightly so.
    What you need is to measure is the diameter of the pencil of parallel(ish) 
    light, output from the eyepiece, so DON'T try to focus it
    down to a spot. Do without the shade. Just put a piece of tracing-paper (or 
    similar) CLOSE UP against the eyepiece, measure the size
    of the resulting spot, and compare it with the size of the objective. The 
    ratio is the magnification. This assumes that there's
    nothing except the objective that restricts the light path through the 
    instrument: no internal baffles getting in the way, and a big
    enough eyepiece to let all the light through. That's usually a good assumption.
    The brightness of the spot on the tracing paper, placed so, can be no brighter 
    than that of the incident sunlight, multiplied by the
    square of the magnification. So a factor of 36 brighter if the telescope was 
    6x. That's without any dark shade intervening. It's
    nothing like the brightness you can get with a burning-glass, a big 
    short-focus lens that converges the sunlight down to a tiny
    spot. Even so, you may feel it's safer if you cover the objective, and just 
    flick the cover away for a fraction of a second. NEVER
    look at the Sun (not through the telescope or even naked-eye) without a proper 
    filter, black as night. Look at the spot on the
    tracing-paper from an angle, NOT directly along the axis of the telescope.
    There's another way to get a rough figure for magnification. Look at something 
    like the strakes along a garden fence, with both eyes
    open; one through the scope and one not. Estimate how many of one will fit one 
    of the other. I am assured it can be done, though not
    by me, as since childhood I have a "lazy eye", that I've never bothered to 
    focus. Luckily, it's my left eye, not the sextant eye.
    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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