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Gary La Pook wrote, with what may be a touch of irony-

I guess then that one cannot see extremely dim objects with the 200 inch
mount palomar telescope for the same reasons that you mentioned.

============================================

It's quite a complex matter, and I hope Gary will give it a bit more thought.

The Mount Palomar, and similar large telescopes, were never intended to be
viewed, through an eyepiece, by the human eye. Nowadays, of course, they
are mostly viewed electronically, but otherwise were used with film. Just
like an enormous camera, rather than the traditional telescope. If, in an
old photo, you see an astronomer peering into an eyepiece of a large
telescope, it's a fair bet that it will be that of a guidance telescope,
not the main instrument.

If Palomar were used with an eyepiece for viewing by a dark-adapted eye
(pupil diameter about 7mm) then with its immense light-collecting mirror of
200 inches, a magnification of about 750 would be needed, to shrink all
that incident light into a small enough bundle to pass through the pupil.
Shrinkage factor of the light pencil, and magnification, go inevitably
together.

Imagine looking at Mars at its closest to the Earth, when it subtends about
0.4 arc-minutes across.

With the naked eye. Mars, even at its closest, is probably rather too small
for the naked eye to resolve as a disc, but let's pretend that it can.

The eye has a focal length of about 20 mm, so a tiny picture of Mars would
be painted on the retina, diameter .0023mm.

Now put in front of the eye the Palomar telescope, with an eyepiece
suitably chosen to give a magnification of x750, necessary to get all the
light in.

The light that this will collect, compared to the unaided eye, will be
greater by the area of the telescope mirror compared with the area of the
eye pupil, (200 inch/ 7mm) squared, or just over half a million times
greater. We're ignoring any losses at the reflecting surfaces.

But now, because of the magnification, Mars subtends an angle 750x greater
than before, or  750 x 0.4 arc minutes or 5 degrees. This will paint a disc
on the retina that's 1.74 mm diameter, which is about 750x bigger than
before, and so about half a million times greater in area.

So, we have half a million times as much light, spread over an image that's
half a million times greater in area. So, to nobody's surprise, the image
of Mars is not a whit brighter than it was before, but a hell of a lot
bigger. The telescope has not increased the brightness, as seen by the eye.
It just can't.

If Gary, or anyone else, doesn't believe me, let him go out in the daytime
with a telescope (perhaps removed from a sextant) or an ocular, or a
night-glass, and look at the sky (but not near the Sun!). Blue-sky or
uniform-cloudy background, it doesn't matter. Neither magnification of
aperture matters. Just note, using one eye through the lens and the other
looking direct, whether the telescope has made the slightest increase in
the brightness of what you see. And if it doesn't make the sky any
brighter, why should it make anything else any brighter? If it doesn't make
the daytime sky brighter, why should it make a night-time scene any
brighter? Answer: it just doesn't.

What makes such a demonstration, using the sky, so convincing is that being
uniform, magnification has no effect on it. Make it bigger, and it still
just looks like sky.

Let me be clear that the above arguments apply to terrestrial scenes, and
diffuse objects such as nebulae, but they DON'T APPLY TO STARS. Because all
stars are nothing more than points of light, that no telescope has ever
been able to resolve, you can magnify a star image as much as you like, and
it won't be spread over a bigger area (except for the effect of optical
imperfections). So increasing magnification really does make a star image
brighter, and not bigger. Which is where big telescopes come in, for
examining faint distant stars.

======================

Now consider the modern telescope as a camera, which is the way it's
usually used.  No longer does all the light have to be squeezed into a
pencil that can enter the pupil of the human eye. There's no eyepiece, the
plate is simply placed at the focus, just as in a camera. In that case, the
notion of angular magnification is meaningless. Instead, you want to know
how far apart in angle two objects have to be for their images to be a
certain distance apart on the photoplate or image transducer, just as in a
camera. That depends on the focal length, and nothing else.

For instance, if you own a standard non-zoom domestic camera with a focal
length of 45 mm, then the Moon, with a subtended angle of about 30
arc-minutes, will always show as 0.4mm diameter. The longer the focal
length, the larger things will be. Any angle in the sky will become a
spacing of     sin(angle) x focal length.

So for the Palomar telescope, with its focal length of about 17 metres, the
moon will be about 150 mm across on the photoplate,  375 x bigger than the
image on the pocket camera, or 140,000 times that area. Any other object,
such as a nebula, will have an increased area in the same proportion.

How much light is available, coming in, to produce that image? Well the
area of the Palomar 200-inch mirror is about 20 square metres. The area of
the lens of the domestic 45mm focal length camera, if set at f/2, is .0016
square metres. So the total light entering the Palomar telescope is about
12,500 times more than that entering the camera. But this has to be spread
over an area which is 140,000 times greater. So, if both camera and
telescope were loaded with the same speed of film,  then to look at, say,
the Andromeda nebula, the domestic camera would need an shorter exposure,
only 1/11 of what's needed at Palomar. Is that a surprise? It surprised me.

What determines the length of exposure, and the ability to capture faint
objects, is simply the aperture/focal length ratio, the familiar /f number
of your camera. The best telescope for capturing faint objects is the
Schmidt, some versions of which have that ratio as high as f/2, just about
the same as some domestic cameras. And the Schmidt and the domestic camera
with the same /f number will be able to capture the same faint objects on
the same grade of film in the same time. The big difference will be that
the image on the camera will be tiny, that on the Schmidt enormous.

===============================
george huxtable wrote:

>Brooke Clarke wrote-
>
>>The devices commonly called "Night Vision" are light amplifiers, not IR
>>based scopes like were used in W.W. II.  They take the existing light
>>and make it brighter.  Although I have not done it, I expect that in the
>>middle of an ocean on a moonless night you could in fact see the horizon
>>with a night vision scope.
>>
>>Astronomers call the optical type of scope you describe a "rich field"
>>scope.  That means that the exit pupil diameter is about 7 mm, which is
>>the diameter of a night adapted eye.  For example a 7x 50 binocular has
>>an objective diameter of 50 mm which when divided by the 7 power
>>magnification yields about 7 mm exit pupil.  Any scope whose objective
>>diameter divided by it's magnification that yields about 7 mm is good
>>for viewing with a dark adapted eye.  For daytime use where the eye's
>>pupil is only a few mm diameter you can use a scope with a smaller exit
>>pupil diameter.
>
>
>What Brooke says about such an optical telescope (and it applies just the
>same to "night binoculars") is quite correct.
>
>But there's an additional point to be made about such optical devices,
>which is often not appreciated, bur was touched on in earlier
>discussion of
>this topic on Nav-l. It's this-
>
>No night-glass or telescope or any other such device can do anything to
>enhance the brightness of a night-scene at the retina, to be any greater
>that what the naked-eye itself sees.
>
>A "night-glass", as Brooke explains, has a big enough objective to
>collect
>all the light that will go into the enlarged pupil of a dark-adapted eye,
>given a certain magnification. In that respect, it's better than a
>"day-glass", which has a much smaller objective for the same
>magnification,
>but is still quite big enough to collect all the light that can go
>into the
>much-smaller eye-pupil in daylight (only about 2mm dia. as opposed to
>7mm).
>In daylight, both these oculars will perform exactly the same. Only at
>night will the night-glass do better. But even then, what you see in a
>night-glass is no brighter than what you can see without it. In fact,
>it's
>somewhat less bright, because of the light-loss inherent in passage
>through
>the glass surfaces.
>
>To take Brooke's example, a x7 night-glass with a 49 mm. objective can
>collect all the incident light falling on it and compress it into a
>narrow
>pencil 7mm. dia, just big enough to fill the pupil of a dark-adapted eye.
>If the objective was bigger than 49mm, then that outgoing pencil would be
>wider than 7mm.,  and light would be wasted in striking the iris rather
>than in passing through the hole. The ratio between the diameters of the
>incoming pencil of parallel light (defined by the size of the objective)
>and the outgoing beam exiting the eyepiece is exactly the same as the
>magnification of the ocular, 7x in that example. Indeed, that's a
>valid and
>simple way to measure the magnification. It's universally true, and
>doesn't
>depend in any way on the details of the optical design.
>
>If we neglect any light loss in transit through the glass or in crossing
>its surfaces, then the night-glass collects 49 times as much light-energy
>to pass into the pupil, compared with the light-energy that would
>enter the
>pupil without the night-glass, simply because of the 49x increase of
>area.  That light now forms an image in the retina. Because of the
>magnification of x7, every object, focussed on the retina, occupies
>49x the
>retinal area than it did without the glass. So the light-energy per unit
>area on the retina, which is the definition of brightness, is no greater
>with the glass than without it.
>
>This conclusion seems to contradict common experience. I agree that when
>you approach a dark harbour, searching for unlit moored craft, a
>night-glass certainly SEEMS to help. In fact, it helps by making the
>images
>bigger, rather than brighter. Surprising, but true. That conclusion
>surprised me when the question arose, when last discussed on this list.
>
>The only way to increase the surface brightness of an image, then, is
>with
>a device that can actually feed additional energy, such as the
>night-vision
>scopes that Brooke refers to.


============================

Geoffrey Kolbe added
"Intensity" is the light flux per unit area per unit solid angle.
"Brightness" is the intensity integrated over all solid angle. Intensity is
what is conserved in any passive optical system. Brightness can indeed be
increased. The obvious example is using a magnifying glass to burn holes in
the school desk on a sunny day...
============================

Yes, my own school desk got a burn in the same way.

There is much confusion about the naming of these quantities, and it would
be useful if it was cleared up. Perhaps, from what Geoffrey says, it has been.

But I have checked with a couple of elderly textbooks on optics, both about
60 years old, and both use the word "brightness" in the same sense that I
have used it, and different from Geoffrey Kolbe's definition. Perhaps I am
just helping to spread that confusion. But I doubt if that choice of word
is actually doing much to undermine the present discussion.

George.



===============================================================
Contact George at george@huxtable.u-net.com ,or by phone +44 1865 820222,
or from within UK 01865 820222.
Or by post- George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13
5HX, UK.

   

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