Re: astronomical vs. terrestial telescopes

["Donald E. Simanek" <dsimanek@EAGLE.LHUP.EDU>]

On Mon, 25 Jan 1999, Carl E. Mungan wrote:

> In class today, I said that terrestial telescopes have the advantages of
> being more compact than astronomical (refracting) telescopes and producing
> erect images. So somebody put up their hand and asked why *all* refracting
> telescopes, and microscopes for that matter, aren't made with a diverging
> rather than a converging eyepiece?

For a given power, the Galilean (terrestrial) telescope is shorter than
the Kelperian (astronomical) telescope, by an amount 2f_e where f_e is the
focal length of the eyelens.

> Frankly I'm not sure of the answer. I said that I supposed that convex
> lenses are cheaper than concave lenses. But are there other reasons -
> eg.  Would a diverging eyepiece have to be larger in diameter than a
> converging eyepiece? (I would think not.) Perhaps the fact that real
> telescopes and microscopes are more complicated than the simple two-lens
> textbook models (in order to minimize aberrations) favors convex lenses?
> (Is there such a thing as aspheric concave lenses? If not, why not?)

I doubt there's much cost difference between convex and concave lenses.

The Keplerian telescope inverts the image, which isn't a problem for
astronomical uses. You just invert the sky maps. Or, at the expense of
increased length of the tube, you can insert a positive "inverting" lens
between objective and eyelens. Or, you can use mirrors or prisms to
re-invert the image, as in true binoculars, terrestrial "spotting" scopes
or high powered scopes for bird-watchers.

The Keplerian telescope has a well-defined exit pupil, a small virtual
aperture through which all the emergent rays pass. This is usually made
smaller than the eye's pupil, so that all the light goes into the eye, and
the eye can be kept at that one fixed position.

The Galilean telescope has no exit pupil, so the outer part of the image
misses going into the eye. The eye pupil size limits the field of view.
However, by moving the position of the eye one can see different parts of
the field, but this is tedious and impractical. Therefore decent fields of
view are obtained only at low powers of 3 or 4. Higher powers are simply
not practical with this design.

> By the way, are reflecting telescopes ever constructed to be erect (by
> using a diverging eyepiece)? And is there such a thing as a reflecting
> microscope?

Not practical, for the lack of an exit pupil would give this the same
disadvantage as the Galilean telescope. Prisms, mirrors, or inverting
positive lenses are used.

Yes, microscope objectives are available which use concave mirrors, much
as short-barrel telephoto lenses do.

> Finally, in lab we measure experimentally the magnification of a telescope
> by holding up a ruler at arm's length and looking through the telescope
> with the other eye. I've tried to do similar things with a microscope, but
> it's hard to do, as are alternatives like trying to draw the size of the
> image on the eyepiece. Is there a workable way to experimentally estimate
> the magnification of an approximately 2X microscope (suitable for a
> low-cost introductory lab)?

It's difficult (read "frustrating") with any decent power microscope. But
with a 2X this might work. You must ensure that the image is at the same
distance as the reference object, perhaps at the near point of the eye,
otherwise the results will be inaccurate due to parallax between the
things you are comparing. Most students find this process difficult to
comprehend and difficult to perform.

I suggest an experiment with the simple magnifier instead, verifying the
usual formulae given in books for the image at the near point, and also
the formula for the image at infinity, then challenge students with the
task of deriving, and verifying, the formula for the simple magnifier with
the image at, say 1 meter. Most students never grasp angular
magnification, nor understand the derivation of the formula for angular
magnification of the simple magnifier. The answers, with discussion, can
be found on my web page in the document "Insight questions". There's also
a discussion of why we define angular magnification as we do, and why we
do it for images at infinity for the telescope, but with images at the
near point of the eye for the microscope.

I'd welcome private e-mail to discuss this if these comments were too
sketchy.

> Dr. Carl E. Mungan, Assistant Professor     http://www.uwf.edu/~cmungan/
> Dept. of Physics, University of West Florida, Pensacola, FL   32514-5751
> office: 850-474-2645 (secretary -2267, FAX -3323) email: cmungan@uwf.edu

        -- Donald

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Donald E. Simanek
dsimanek@eagle.lhup.edu                 http://www.lhup.edu/~dsimanek
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