The resolving power of a telescope is another very important factor. It increases with increasing aperture. If the telescope has a high resolution, fine detail can be seen in non-stellar astronomical objects. The resolution is defined as the ability to individually and recognizably image two closely spaced objects.
In practice this means that two individual stars in a double star, separated by a certain angular distance, can be separated. So imagine: You are trying to observe a double star and to see two fine stellar points directly next to each other.
If the resolution is not sufficient for this particular star, then you would just see a single point or perhaps a slightly elongated structure.

The narrower the angle of a double star or the closer together the details on a planet, the more aperture is required to achieve a higher resolution, and be able to separate the objects. The separate resolution of two objects is often called their separation or ‘minimum separability’.

The resolving power of the naked eye is about one minute of arc during the day and about 2 minutes of arc at night. You can even separate quite a few double stars with the naked eye, such as the ‘Horse and Rider’ in the Big Dipper.

Perhaps your optician mentioned the term visual acuity? Opticians are happy when you achieve optimal visual acuity, and will speak of a visual acuity of 1.0. This value corresponds to a resolution of one minute of arc.

However, some people do not achieve such a high resolution while others even achieve a slightly higher resolution - which is in the nature of things and is completely normal.
The large apertures of telescopes mean they can achieve a very high resolution. While a 50mm telescope has a resolution of about 2.7 arc seconds, a 200mm telescope has a resolution of 0.7 seconds of arc. With these resolutions, these telescopes can cleanly separate two stars that have these separations. One factor in the resolution is the size of the Airy disk resulting in the telescope. The higher the resolution of a telescope is, the smaller the size of the Airy disk appearing in the telescope. The resolution is relatively easy to calculate:

A = 138 / Obj

A = resolution, Obj = aperture of the telescope [in mm]

This calculation is a formula according to Rayleigh and gives the separation which, for example, a binary star system can still clearly be split into its individual stars. 

Of course these are theoretical values ​​that are not 100% the same in practice. This is because, usually, the resolving power of a telescope is limited by the turbulence in the atmosphere to about 1 arc second. This means that telescopes that have an aperture of more than about 120mm bring no real benefit in this area.

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