For both these types of telescope, the resolution (or resolving power) is inversely proportional to the wavelength of the light that it captures, as well as being proportional to the size of the telescope’s ‘aperture’. The aperture size is usually equivalent to the size of the primary mirror in a reflecting telescope, or the objective lens in a refractor. This is not always the case, however, as sometimes only the centre region of a telescope’s mirror will be used, to reduce the effects of spherical aberration, perhaps (see below).
For a circular aperture, the maximum theoretical resolution is given by the formula:
θ = 1.22 λ / D
Where λ is the wavelength of light, D is the diameter of the telescope’s aperture (usually the diameter of the primary mirror or lens) and θ is the maximum angular separation between two point sources of light, or other features, that can be resolved by the telescope.
The value of θ can be calculated for a telescope with diameter D using a typical wavelength for visible light λ. Two stars that are closer together in the sky than this angle, will not appear as two separate objects when viewed through the telescope. Nor will surface features on a planet or the Moon, for example, that are smaller than this angle, be resolvable, no matter how powerful the eyepiece that is being used, or the manufacturer’s stated magnifying power of the telescope.
Of course the precision to which a telescope’s optical surfaces and lenses have been manufactured will also affect the image quality of a telescope, and viewing conditions, such as turbulence in the atmosphere, also affect a telescope’s ability to resolve fine details. The angle θ represents the absolute maximum limit of a telescope’s theoretical resolution, rather than a typical achievable resolution. For the large telescopes used by professional astronomers, the effect of atmospheric turbulence is an extremely important limiting factor in a telescope’s ability to resolve detail. This is why they are often constructed at high altitudes where the atmosphere is thinner and stiller, and why the Hubble Space Telescope can outperform much larger ground-based telescopes. However, modern telescopes can also use adaptive optics as way to counter the effects of atmospheric turbulence.
Telescopes are also used to capture electromagnetic radiation at wavelengths outside of the visible spectrum. However, the longer the wavelength of the electromagnetic radiation being studied, the larger the aperture required to produce an image to an equivalent resolution. This is why the giant parabolic dishes of radio telescopes are necessary to provide an adequate resolution to study the universe at radio wavelengths, which are much longer than the wavelengths of visible light.
A telescope’s ‘power’ usually refers to its magnification. This should not be confused with its resolving power or resolution, however, which depends on the telescope’s aperture size, as described above.
The magnification that a telescope provides depends on the eyepiece that is used, as well as the focal length of the telescope, so a telescope with a small primary mirror or lens can provide a highly magnified image, but its ability to produce a sharper more-detailed image, will not improve with the use of a more powerful eyepeice. The image obtained with a more powerful eyepiece will just be larger, with a smaller field of view, but less sharp. That said, a high-power eyepiece will provide a more magnified image that can often help the eye to discern smaller features.
Since the power of a telescope is also dependent on its focal length, the same eyepiece used with different telescopes can produce images of different magnifications, even though they might have the same-sized primary mirrors or lenses. The length of the telescope’s tube usually provides an indication of the focal length of the telescope, with shorter-tubed telescopes often having a more curved mirror, and hence a shorter focal length, giving a more magnified view than a longer telescope with the same eyepiece. Note that this only applies for telescopes with the same optical layout, such as two Newtonian telescopes, or two Schmidt-Cassegrains – the latter generally needing shorter tubes because the light is deflected back down the tube one more time before it reaches the eyepiece (see Reflector Telescopes).
It’s important to remember, when buying an amateur telescope, that the size of the primary mirror or lens, which determines the intrinsic maximum resolution, is usually much more important than the ‘power’ rating of the telescope, which will depend on the eyepiece as well as the focal length of the telescope.