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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.


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01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
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