Re: Stupid question about magnification

canopus56 wrote:
> nick wrote:
>> Of course, stars will
> > project an image that is much smaller than diffraction disc, so that it
> > can't be seen under any magnification. > Vlad
>
> But the stars are seen and do not simply disappear at effectively
> infinite distants because the size of their diffraction disk becomes
> too small. That they do not disappear is what a "point source" is all
> about.

No one said they disapear; we do see diffraction pattern which,
obviously, can't be considered an image since its form is independent
of object's actual features. "Point-like" comes from the fact that
object's
geometrical image size is smaller than diffraction disc - not that it
is
infinitely small. For instance, angular diameter of Betelgeuse, which
is
131 parsec far away, is 0.05 arc seconds. This means that we'd need
~4m aperture in near-ideal conditions to see its actual image beginning

to emerge from the diffraction disc.

>
> IMHO, what happens at one parsec is this:
>
> 1 parsec ~ 3.08 x 10^16 m
> 1 parsec ~ 3.08 x 10^19 millimeters
>
> M = f / ( o - f )
>
> M = 1000 / ( 3.08x10^19 - 1000)
>
> - which is - as a matter of practical computation - undefined division
> by zero.

We can readily reduce it to M=f/o (makes it simpler and doesn't make
any difference) which gives M=1/(3.08x10^16). Far from "undefined".
For a moderately large star of, say, 10 times the Sun diameter, it
comes to nearly 0.1 arc second angular diameter.
>
> This means that the thin lens equation for magnification, that you
> applied out to the distance of the Sun, breaks down and is no longer an
> accurate model for what is observed. So, we switch to another
> mathematical model that better describes what happens. For lack of a
> better term, I'll call it the "paraxial imaging scaling" equation
> discussed up thread.
>
> h = lambda * fl / k Eq. 1 per Sigdwick (1971 3rd ed) at 52 and 346.
>
>
> where h is the linear height of the object at prime focus, lambda is
> the angular size of the object, k is a conversion factor to change the
> angular size of the object into radians and fl is the focal length.
>
It is the same thing, different packaging. The angular object size
(btw., it is "theta", not "lambda") directly reflects object
size/distance
relationship.

> In this model, the dimensionless scalar of magnification or "power"
> can't be computed and, as Chris has correctly pointed out, isn't
> defined in formal optics - only image scale is defined.

I wouldn't say that you and Chris are following the same path.
You two don't even share a common concept. His remarks -
at present - are about the importance and/or appropriateness of the
magnification concept, not its validity. You are simply truying to
prove it wrong. Have fun...

Vlad

.