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The angular resolution of a telescope is given by $\frac{1.22\lambda}{D}$.

This should mean that the smaller the aperture D, the higher the angular resolution. But it is exactly the opposite - why?

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Part of the confusion stems from the words used. "higher" resolution doesn't mean better, it means only bigger objects can be resolved; but we want to be able to resolve small objects, such as the angular distance between a pair of double stars. So small is better in this situation.

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  • $\begingroup$ "Higher resolution" usually does mean better. (If you want a plausible way to think about it, "higher" resolution means you can resolve higher spatial frequencies, which means smaller angular sizes.) $\endgroup$ – Peter Erwin May 23 '18 at 20:46
  • $\begingroup$ Peter Erwin: well I think that given how the word is commonly used, it’s not a surprise that the OP found the use of “higher” in this context confusing. $\endgroup$ – Dr Chuck May 23 '18 at 21:49
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The angular resolution only tells you your ability to distinguish ("resolve") two separate points of light. For example, your ability to distinguish the two distinct headlamps on a car from being a single light in the distance.

The angular magnification has nothing to do with the angular resolution: it is determined by the focal lengths of your primary and objective, and the eyepiece if applicable.

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Your formula is correct. In the absence of instrumental effects or blurring of the atmosphere, it gives (approximately) the minimum angular separation between two objects that can be resolved. The larger this is, the worse your telescope is. You want the resolution to be small.

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