Re: Telescopes - Diffraction limit

[Bernard Cleyet <anngeorg@PACBELL.NET>]

I haven't been able to follow the below, so my comment may be redundant.

Jenkins and white (3rd. Ed. pp 304 ff.) point out that there is a min.
eyepiece magnification for the resolution of the objective to be
realized.  i.e. the exit pupil must be equal or smaller than the eye's
pupil.  The "normal" magnification is when the ocular's pupil diameter
is equal to the eye's in the formula:  M = D/d  (D is diameter of
objective pupil, d is ocular's.)  D/d(eye) = [1.22 lamda/d(eye)] / [1.22
lambda/D] = theta(prime) / theta.   Thus if d (exit pupil) is made >
d(eye), then theta(ocular) will be < theta (eye) and the images will
cease to be resolved by the eye even thought resolved in the focal plane
of the objective.  This explains why my Celestron instruction manual has
a min. ocular magnification in addition to the (obvious) max.

bc

John Mallinckrodt wrote:

> >         Without working through this carefully, my first
> > thought is that the angular separation is what is
> > involved in the deification limit.  The primary
> > mirror or lens has increased the angular
> > separation viewed by the eyepiece.
>
> God or no God, I think Roger is right here.  The angular
> magnification of the scene provided to any element in the optical
> system is
>
>      M_ang = f_obj/f
>
> where f_obj is the focal length of the objective lens and f is the
> focal length of the element.  The angular resolution of the system
> should, therefore, be determined (primarily) by that of the weakest
> link after correcting for the angular magnification factor for that
> link.  That is
>
>     angular resolution = maximum[(1.22 lambda/f_obj)*(f/D)]
>
> where the expression in brackets is evaluated for each element using
> its focal length f and diameter D.
>
> For instance, in the case of a telescope with a 150 mm aperture
> operating at a power of 50, the eyepiece would need to be at least 3
> mm in diameter to prevent it from degrading the angular resolution.
>
> --
>     A. John Mallinckrodt        http://www.csupomona.edu/~ajm
>     Professor of Physics      mailto:ajm@csupomona.edu
>     Physics Department         voice:909-869-4054
>     Cal Poly Pomona              fax:909-869-5090
>     Pomona, CA 91768-4031     office:Building 8, Room 223