Which is a better way to increase magnification - by choosing an eyepiece of lesser focal length or by choosing a telescope with higher focal length?

Question

Magnification of a telescope = (focal length of telescope / focal length of the eyepiece being used) $$M=\frac{f_{objective}}{f_{eyepiece}}$$

If I want 75 X magnification and the following are the two ways being considered for obtaining that magnification, which one is better? What are the trade-offs and effects on the quality of observation? Where will I get a sharper image?

Method 1: Use telescope of 600mm focal length and an eyepiece of 8mm - giving magnification = 75 X $$M = \frac{600\,mm}{8\,mm}=75$$

Method 2: Use telescope of 1200mm focal length and an eyepiece of 16mm - giving magnification = 75 X $$M = \frac{1200\,mm}{16\,mm}=75$$

Assume that the telescope aperture is the same in both cases.

Any references are also welcome.

Does this answer your question? Difference between first (focal length (fl.) 500 mm, ocular (o.) 10 mm) and second telescope (fl. 1000 mm, o. 20 mm)? (both 50 x) — User123, Oct 28 '20 at 17:04
Welcome to Stack Exchange! This is an excellent first question, don't worry that it was closed as a duplicate, it's just that an existing answer seems to answer your question as well. Your post will help to direct future readers to that answer. If you think this is sufficiently different that it should be reopened so it can receive a different answer, go ahead and modify the question accordingly, or post a new and different quesiton. — uhoh, Oct 29 '20 at 23:17

Which is a better way to increase magnification - by choosing an eyepiece of lesser focal length or by choosing a telescope with higher focal length?

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