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Magnification is defined as $f_{objectiv}/f_{ocular}$. If I had the first telescope with the focal length of 500 mm, ocular 10 mm and second telescope with the focal length of 1000 mm, ocular 20 mm, is there a difference between them? Both of them has 50x magnification.

I want to know if there is any difference in the quality of image, etc.

Thank you for all!

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  • $\begingroup$ Can you add each telescope's objective diameter (aperture) to the question? $\endgroup$
    – Mike G
    Aug 1, 2019 at 14:21
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    $\begingroup$ All else being equal (same aperture, same quality of optics) there won't be a difference between them. But long f/ratio (longer focal length with same aperture) does make it easier to fabricate a quality lens/mirror. $\endgroup$
    – antlersoft
    Aug 1, 2019 at 15:01
  • $\begingroup$ @MikeG I am centered only to magnification. $\endgroup$
    – User123
    Aug 1, 2019 at 17:22

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The larger the entrance aperture, the greater the light-collecting capability. Now, you didn't specify that, but that does matter in your final choice.

Next, as the comments suggest, the choice of optics depends on the cost vs. quality trades. You want not only a given magnification but also as little coma, distortion, spherical aberration, and so on. At a very simple (and probably unrealistic) level, the longer lens pair (1000,20) might be easier to fabricate with low aberrations. In real life, we quickly descend into multi-element systems, or cemented doublet designs, and so on.

I'm guessing you are talking about a Keplerian design (two positive lenses), in which case consider how much longer the physical telescope is in the 1000-20 case.

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  • $\begingroup$ This is a subtle point but I think that this light collection capability only matters for unresolved objects like stars, moons (other than our own) asteroids and unresolved planets. I don't think (but am not sure that) the double-everything system will make an extended object like Jupiter or the Moon any brighter at the same magnification. Instead, the diameter of the light at the eyepiece's exit pupil (where we place our own eye's entrance pupil) will be twice as wide, and may simply be wider than our 6mm max pupil. It might matter for eyepiece projection or astrophotography but not viewing $\endgroup$
    – uhoh
    Oct 29, 2020 at 2:15
  • $\begingroup$ For more on conservation of etendue see answer(s) to Can a telescope ever increase the apparent luminance of an extended object? $\endgroup$
    – uhoh
    Oct 29, 2020 at 2:16
  • $\begingroup$ @uhoh I believe the exit pupil would be the same in either case. $\endgroup$
    – Mike G
    Oct 29, 2020 at 10:20
  • $\begingroup$ @MikeG my comment carefully specifies a "double-everything system" and so is self-contained and I think correct as written. I see that you asked about the aperture in your comment and received only an unhelpful response so far. $\endgroup$
    – uhoh
    Oct 29, 2020 at 11:11
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    $\begingroup$ @uhoh I had confused this Q with the new one flagged as a dup. $\endgroup$
    – Mike G
    Oct 29, 2020 at 15:09

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