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I know that the maximum (useful) magnification is limited by the diffraction limit, but I was not able to find numbers for the highest useful magnification factors using modern large telescopes.

How much magnification is possible, e.g. using the E-ELT?

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Well when applied to visual telescopes, the practical "magnification" limit, which is what you asked for, would be that angular magnification, which magnifies the diffraction limited image of the telescope up to the resolution limit of the eye.

Now a telescope of about 4.5 inches aperture resolves about one second of arc, so a one inch telescope would resolve about 4.5 seconds of arc.

The human eye in a relaxed state can resolve about one minute of arc, so it would take a magnification of about 33.3 to bring the star image up to one minute of arc. But that is an extreme resolution for the eye and is strainful, so about 1.5 minutes of arc is a more robust viewing condition, which means a magnification of about 50 (angular mag) for a one inch telescope.

Lots of telescope making books, have suggested 50 per inch of aperture as the maximum useful visuaual magnification. For non visual sensors, you could go above that, as for example with your mega-telescopes.

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  • $\begingroup$ Ok, thinking of the E-ELT (almost 40m aperture = 1575 inches), this would imply roughly impressive 80.000x magnification. Do you thin that this rule of thumb can be applied here? $\endgroup$ – MrD Sep 20 '13 at 10:06
  • $\begingroup$ Well remember that rule of thumb is largely a consequence of the human eye resolution; any more visual mag, is just bigger fuzzy images. So with the E-ELT which is not likely to be used visually, I doubt the rule is useful. Some of the big telescopes operate at very long focal lengths at the Coude focus; but for special reasons, usually not imaging related (spectroscopy). $\endgroup$ – user26165 Sep 20 '13 at 22:19
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Typically a telescope is judged by it's angular resolution. As a benchmark, the angular resolution of the Hubble Space Telescope is 0.05 arcseconds. The E-ELT is a combination of several different types of telescope, and the very best of these should have an angular resolution of 0.001 arc seconds - 50 times better than Hubble.

The most distant galaxy ever observed is about 13.4 billion light years away (well, it was when the light we see left it). At that distance a resolution of 0.001 arc seconds corresponds to about 64 light years.

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  • $\begingroup$ If the light has traveled 13.4 billion years to get to us, it was significantly (closer( than that when the light was emitted, as not only the distance already traveled, but also the distance it hasn't traveled yet, is expanding. $\endgroup$ – Thriveth Sep 17 '13 at 19:43

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