Modern astronomy begins with the telescope. Without that invention, astronomy would never get past the naked eye phase, which is really quite limiting. Your eye collects all the light that will go through a hole about 1/4 inch in diameter - that's the diameter of the pupil at maximum opening. As far as scientific observations go, the eye is a lousy detector. Modern astronomers do not look through their telescopes. In fact, some telescopes, like the Hobby-Eberly Telescope at McDonald Observatory cannot be used in this way. There is no way to look through it.
How many stars can you see through that 1/4-inch hole? Your eyes alone see somewhere in the 4,000 to 5,000 range. If you sometime get tempted to wax poetic about the millions of stars in a clear night sky, restrain yourself. A few thousand is more like it. A planetarium can produce a lovely night sky illusion with 2,000 stars.
Astronomically speaking, the telescopes primary function is to collect light. As the objects studied by astronomers get more distant and fainter, larger and larger telescopes are needed to get enough light to study. The basic job is to collect the light and bring it to a focus to make an image of the distant object. That's why astronomical telescopes are described as "light buckets." Also note that the distance from the objective lens or mirror to the image point is called the Focal Length (F).
The basic visual telescope has two optical elements - the objective and the eye lens. The objective can be a lens or a concave mirror; either will work perfectly well. A refracting telescope uses a lens for its objective; a reflecting telescope uses a concave mirror. Both work.
The first useful form of reflecting telescope was invented by Sir Isaac Newton. It uses a small diagonal mirror to bounce the converging beam out the side of the telscope, thereby solving the problem of getting your head in the way. This form of telescope is known as Newtonian. It is optically simple and is easy to make, which is why amateur astronomers have made so many of them. A simple Newtonian is the easiest type of telescope to build. This one (a commercially made model) is one that an amateur astronomer might have. Here is a small refracting telescope.
Any telescope which uses a mirror to collect the light is a reflector. Variations in the light path after reflection by the primary concave mirror amount to variations on a theme. There are several forms of reflecting telescope. Look at Figure 3.5.
The largest refracting telescope in the world is at Yerkes observatory in Wisconsin. It went into service in the spring of 1897 after 5 years of construction. The objective lens is 40 inches (about 1 meter) in diameter. As telescopes go, this is not huge. Reflecting telescopes, using multiple mirror segments, have now reached 10 meters diameter, or 10 times the diameter of the Yerkes refractor. Ten times the diameter means 100 (that's one hundred) times the area for collecting light.
All new large telescopes today are reflectors. There are reasons why large refractors are not built.
Whatever the telescope, its job is to collect light and bring it to a focus making an image. The bigger the mirror, the more light will be in the image.
Once you have that image, you have a choice of a number of things to do with it. If you place a light-sensitive film where the image is, you can record the image - this is photography. You can place any one of several different types of light detector at the image and record data digitally. Along this line you might use one of the following.
How much does the telescope magnify when you look through it? Simply divide the
focal length of the objective (F) by the focal length of the eye lens (F).
power = F/f
The quotient is the magnifying power.
The two properties we are interested in are light gathering power and resolution. Both are related to the aperture, or diameter, of the objective lens or mirror. Magnifying power applies only to telescopes used visually and is easily calculated. Simply find the focal length of the objective lens or mirror, then determine the focal length of the eye lens (normally imprinted on the eyepiece, or ocular. Divide the objective focal length by the eyepiece focal length to get the magnifying power. Since eyepieces are interchangeable, the magnifying power of the telescope can obviously be changed easily.
The light-gathering power of a lens or mirror is a function of its area. A mirror 24 inches in diameter collects 4 times as much light as one 12 inches in diameter. The area is proportional to the radius squared. Taking the spectrum of an object requires spreading the light over some area to record the different wavelengths. This requires more light than simply taking an image, so spectroscopy requires large telescopes. This is particularly true as the objects being studied get fainter.
The resolving power of the telescope is its ability to show separate images of things that are very close toether. This power has an inverse relation to aperture (lens/mirror diameter) and the wavelength of the light. Here are some illustrations.
One of the biggest limits to telescope performance is the air that the telescope must look through. Air moves and has different temperatures at different altitudes. This combination causes problems for astronomers. You have likely noticed this but not thought about it. To refresh your memory, go outside on some clear night and watch the stars twinkling. In fact, stars don't twinkle. The effect is caused by turbulence in our atmosphere. The tiny refraction (bending) of starlight (or anything-else light) as it passes through the atmosphere causes the image to spread out and twinkle, seriously reducing the resolving power of the telescope. A telescope may have a diffraction limit of 0.05" of arc and yet be limited to 0.5" to 1" by the atmosphere. This effect of the atmosphere is called "seeing." That's why the Hubble Space Telescope is in orbit - it is above the atmosphere and does not have the problem. These images show turbulence effects by telescope diameter. Larger telescopes are affected more than small ones.
The other atmospheric property we need to understand is transparency. It is, very simply, an indicator of how much humidity, dust and other crud is in the air. Poor transparency dims the light and makes faint things hard (or impossible!) to see.
To review - the visual properties of the atmosphere have names - transparency and seeing. If the air is not clear, but rather full of smog and dust and other crud, the transparency is poor and you can't see much. Bad seeing manifests itself by making the stars twinkle. The best conditions have superb seeing AND transparency; the air is very clear and very still.
Here are web sites for some large telescopes. Some of these are really large.