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Here are some old references I have on file:

Jacobs, D.H., "Fundamentals of Optical Engineering", McGraw Hill, NY, 1943

Martin, I.C.,  Optical Measuring Instruments", Van Norstrand, NY, 1924

Reichart, R.J. & E., "Binoculars & Scopes", Amphoto, Garden City, 2 Ed. 1966

"Binoculars", Consumer Reports, Nov, 1971, pp 724-727

Nothing I recall differs from George H's analysis, but some of these books
have mathematical equations which describe some of the desired
characteristics of telescopes which include Relative Light Efficiency,
Theoretical Relative Brightness, Twilight Factor, Light Transmission,
importance of coatings, and so on.

Joel Jacobs


----- Original Message -----
From: "George Huxtable" 
To: 
Sent: Tuesday, May 04, 2004 4:09 PM
Subject: Re: Sextant optics


> 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.
>
> George.
>
>
> ================================================================
> 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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