How much you can see through an astronomical telescope depends on a lot of things, but the two most important factors are the quality of the optics and the diameter of the primary lens or mirror.

If you buy a toy telescope in a department store, you shouldn't expect to see much. The lenses and mirrors might not be made very accurately, and they might even be made of plastic. Astronomers custom build their telescopes, grinding the optical surfaces to high precision so there is a minimum of distortion. Nevertheless, some poorly made astronomical telescopes do not produce good images and astronomers sometimes refer to them as light buckets.

The other factor is the diameter of the primary lens or mirror. Because light has wavelike characteristics, when it is brought to a focus, every bright point of light in the image is surrounded by tiny rings of light called diffraction fringes. Consult your textbook for a figure showing diffraction fringes. You don't usually see diffraction fringes in daily life because they are so small and because optical surfaces such as the lens in your eye are not of high enough quality. In a really fine astronomical telescope, however, the fringes can be visible.

The size of the diffraction fringes depends on the diameter of the primary lens or mirror. The larger in diameter the telescope, the smaller are the diffraction fringes. If you were looking at two stars close to each other, you might be able to see them as two separate points of light in a large telescope, but in a small telescope the diffraction fringes might be so large they would overlap and the pair of stars would look like a single point of light.

In the animation, you can see a pair of stars, and you can adjust the diameter of the telescope. (Notice that the eyepiece of the telescope is not shown for simplicity.) You can't see the individual diffraction fringes around the star images; the fringes blur together to make the stars look like fuzzy balls. So you know the telescope is not of the very highest quality. As you make the telescope larger, the fringes get smaller, and you see the fuzzy images of the stars shrink. If you make the telescope smaller, the fuzzy images get larger, and you can imagine how difficult it would be to see these two stars as separate images with an even smaller telescope.

That, by the way, is why you can't measure the diameters of stars by looking at them through a telescope. The diameter of the images in the telescope is set by diffraction and not by the actual diameters of the stars. That is, the stars are much smaller in diameter than the diameter of the diffraction images. In the animation, the brighter star has a larger image because its fringes are brighter and you can see more of them, not because it is a larger star.

The resolution of a telescope, its ability to reveal fine detail, depends on the quality of the optics, but it also depends on the diameter of the telescope. Larger telescopes produce smaller diffraction fringes and sharper images. The resolving power of a telescope is the angular separation between two stars that are just barely visible through the telescope as separate images. For telescopes focusing visible light, the resolving power in arc seconds equals 0.113 divided by the diameter of the telescope in meters.