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I'm a little confused. Could you help me?

The question is: if we increase the radius of a telescope twice, how much does the light gathering power change? What about resolution?

Does it increase 22-fold?

For second part, I know as the diameter of the telescope's objective increases, the resolving power increases.

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The collecting area of a telescope is roughly proportional to the square of its radius (for a circular aperture). I say roughly because you also have to factor in the small fraction of light blocked by the secondary if we are talking about reflecting telescopes.

In principle the angular resolution decreases as the reciprocal of the radius (that is, the smallest resolvable angle gets smaller). In practice, this may not be the case for ground-based telescopes without adaptive optics capabilities, where the smallest resolvable angle could be determined (for large telescopes at least) by turbulence in the atmosphere (a.k.a. the seeing).

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  • $\begingroup$ Thank you for your great answer. I have one more little question. The question said "increase the radius of telescope twice" so should i think new radius as "2x" and the light gathering power will be "(2x)^2" ? $\endgroup$
    – Basak
    Commented Dec 26, 2017 at 18:53
  • $\begingroup$ Yes, that's exactly how it works. $\endgroup$
    – Phiteros
    Commented Dec 26, 2017 at 21:36

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