Re: Stupid question about magnification

In article <d4v1t1del4t41meago5oclmcjh8306hi8l@xxxxxxx>,
Chris L Peterson <clp@xxxxxxxxxxxxxxxxxx> wrote:

> On 20 Jan 2006 06:39:27 -0800, "nick" <svla@xxxxxxx> wrote:
>
>> I'll tell you what is the use of it, even if it should be obvious for a
>> while. It is necessary to understand how telescopes work (magnify).
>> Telescope optical power (magnification) is a product of optical power
>> (magnification) of the objective, and optical power (magnification) of
>> the eyepiece.
>
> I've been designing optics for 25 years, and I've never used this
> concept to either understand how telescopes work, or to design their
> optics. Understand I'm not saying it is untrue, only that it is a poor
> way to think about an optical problem.

It's not necessarily a poor way to think about magnification in
telescopes like that, but it's definitely an uncommon way. Your 25
years experience in designing optics can actually be an obstacle to
view this in an alternate way.

Have you ever dabbled with microscopes? In microscopy, it is common
practice to assign separate magnification for the objective and the
eyepiece. Here one uses a convention: the closest distance for
comfortable viewing by a normal human eye, without using any optical
aid, is 25 cm (approximately 10 inches).

The magnification of an eyepiece is then defined as:

25 cm divided by the focal length of the eyepiece

The magnification of the microscope objective can be defined more
objectively: it is of course the size of the image of the object (at
the focus of the eyepiece) divided by the size of the object itself.

So if you have a microscope with an objective with 10x magnification,
and if you use a 12.5 mm eyepiece (which has 25 cm / 1.25 cm = 20x
magnification), that microscope will get 200x magnification.

And if you use that 12.5 mm eyepiece by itself, as a magnifying glass,
it will have 20x magnification. With magnifying glasses one uses the
same convension as with microscopes: the unmagnified angular size of
the object is considered to be when the object is viewed at a distance
of 25 cm.

-----------------------------------------------------------------------

Now, let's apply this principle to telescopes. Let's assume we have a
telescope with an objective lens having 1500 mm focal length. Let's
assume we use our 12.5 mm eyepiece at the telescope instead of at the
microscope. It's reasonable to assume that the magnification of the
eyepiece remains unchanged, i.e. that it still is 20x.

The magnification of the telescope will of course be 120x (1500 mm
divided by 12.5 mm, using the standard formula for telescope
magnification).

Since the telescope magnifies 120x, and the eyepiece magnifies 20x,
it is reasonable to assume that the objective alone magnifies 6x.
Now we can multiply the magnification of the objective with the
magnification of the eyepiece, to get the magnification of the
whole telescope. Just like we do on a microscope.

Here I hear you object: "It is not reasonable to say that a 1500 mm
f.l. objective has a magnification of 6x !!!!!" -- but please read on.

We have:

1500 mm / 250 mm = 6

and therefore the magnification of the telescope objective is 6x.

"But where did that 250 mm get from?", I hear you cry. Well, 250 mm
is 25 cm, that standard distance for viewing an object confortably as
close as possible for someone with normal vision and without optical
aid. The "object" to be viewed is here the image created by the
objective lens at prime focus (since the eyepiece is removed, we do
have a prime focus). Therefore a 1500 mm f.l. telescope objective
lens alone has a magnification of 6x -- comparable to the
magnification of a pair of small binoculars.


Thus we get, for a telescope:


Magnification of objective = focal length of objective / 25 cm

Magnification of eyepiece = 25 cm / focal length of eyepiece


Magnification of telescope = magnific_objective * magnific_eyepiece

Magnific_telescope = ( F_L_objective / 25_cm ) * ( 25_cm / F_L_eyepiece )

Magnific_telescope = F_L_objective / F_L_eyepiece



You may find this view unusual - but it works! We can assign separate
magnifications to the telescope objective and telescope eyepiece, and by
multiplying them with one another we get the traditional standard formula
for the whole telescope.

And the separate magnifications of the objective and the eyepiece are
meaningful. The magnification of the eyepiece is how much it will
magnify if used by itself as a magnifying glass. And the
magnification of the objective is how much it will magnify if it is
used by itself to produce an image at its primary focus and if that
image is viewed by a human eye at a distance of 25 cm -- the standard
closest distance for comfortable viewing by a human eye.


No magic is involved here, and the traditional telescope formulas still
work. It's only a perhaps somewhat different way to view the issue of
magnification. And that view is at least somewhat useful - the magnification
figures assugned separately to the telescope objective and eyepiece are
not meaningless.



--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://stjarnhimlen.se/
.

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