# Telescope

The word telescope comes from the the ancient Greek words for "far seeing", which is a pretty good description of what a telescope does. Various types of telescopes are used throughout the electromagnetic spectrum though this article will discuss the basic types of optical telescopes.

## Telescope Basics

Optical telescopes come in many shapes, sizes and designs. In general there are three parameters used to describe all telescopes:

• aperture - the diameter of the primary lens or mirror
• focal length - the focal length of the optical system, in other words the apparent distance from the primary lens or mirror to the point where an image is in focus.
• f ratio - the focal length divided by the aperture, this is a measure of how photographically "fast" the telescope is. Smaller f ratios require shorter exposures with a camera to create an image.

Regardless of design or parameters, in astronomy the telescope performs three basic functions, collecting light, resolving images and magnification of images.

### Collecting Light

First it collects light. The larger the aperture of the telescope, the more light it collects and hence the dimmer the objects it can see. The dimmest a particular telescope can see is called the limiting magnitude. Though the aperture of the telescope is the major factor in limiting magnitude, there are other factors that can affect this such as sky brightness.

### Resolving Images

The second thing a telescope allows the astronomer to do is resolve images. That is, it allows the astronomer to see fine detail in an object or to see two objects that are close together as separate objects. Again the larger the aperture the better the resolving power of the telescope or the closer together objects can be. The theoretical resolution limit of a telescope is called the Dawes limit, after the British astronomer who discovered it. This empirical relationship describes how far apart two stars have to be to be seen with a particular aperture:

$R=\frac{4.56}{D}$

Where R is the resolution in arc seconds and D is the aperture of the telescope in inches.

### Magnifying Images

The third thing a telescope does is the thing that most people think of when they think of telescopes, that is magnifying an image or making an object look closer. The magnification of a telescope is related to the focal length of the telescope and the focal length of the eyepiece used to view the object. By changing the eyepiece of a telescope one can change the magnification. Magnification is given by:

$M=\frac{F}{f}$

Where M is the magnification, F is the focal length of the telescope and f is the focal length of the eyepiece. So for a telescope with a 1500mm focal length, using a 25mm eyepiece will produce a magnification of 60x.

There is a limit to how much magnification you can get out of a telescope. The smaller the diameter of the telescope the lower this limit is due to the resolution of the telescope. There comes a point where more magnification just magnifies the lack of resolution and doesn't produce a better image. The maximum useful magnification for a telescope is between 40 and 50 times the aperture of the telescope in inches[1]. So a 5" telescope has a maximum useful magnification of between 200x and 250x. Anything more than this does not provide a better image since the resolution is not there.

## Telescope Types

There are many optical designs for telescopes but there are only three basic types:

• refracting telescopes
• reflecting telescopes

### Refracting Telescopes

Refracting telescopes, often called refractors, use lenses to form an images. In a basic refractor, the primary objective is a large lens at the front of the telescope. The light from the object comes through the lens, is refracted (bent) and comes to a focus somewhere behind the lens where the eyepiece or imager is located.

Refracting Telescope

Refractors have the disadvantage in that they suffer from chromatic aberration, that is light of different colours focus at different places. Modern refractors are designed to reduce this problem and a good modern refractor can provide very good views.

Refractors also tend to be quite expensive per unit of aperture as many surfaces of optically clear glass must be ground to provide aberration limited views. This means that most refractors owned by amateurs are small, 4" or less in diameter. Despite these problems refractors are prized by planetary observers as the refracting telescope provides good contrast which is needed for planetary observation. Refractors also don't have a central obstruction as reflectors do as the optical system is straight through, which limits diffraction around objects caused by the secondary mirror of the reflector.

### Reflecting Telescopes

Reflecting telescopes avoid the problem of chromatic aberration by avoiding the use of a lens as a primary objective. In it's place, a parabolic mirror is placed at one end of the telescope and the light is then brought to a focus at some point outside of the telescope. There are many types of reflecting telescopes, the type depending on where the light is brought to a focus. Two common types are the Newtonian and the Cassegrain.

Newtonian Reflecting Telescope

Apart from having no chromatic aberration, reflecting telescopes also have the advantage of being cheaper per unit aperture than refracting telescopes as there are fewer surfaces that need to be polished. In fact, many amateur astronomers routinely build Newtonian telescopes from scratch. There was a time when amateurs would even grind their own mirrors, but with the advent of relatively inexpensive, commercially available mirrors, there is less of this.

Reflecting telescopes do suffer from coma, that is objects near the edge of the field of view tend to be drawn out into teardrop shapes. This causes images of objects that cover most of the field of view to degrade towards the edge of the field. Reflecting telescopes also have a central obstruction in the form of the secondary mirror. This mirror and its support cause diffraction in the image which doesn't exist in the refractor.

Catadioptric telescopes are a mix between refracting and reflecting telescopes. A corrector plate is placed in front of the primary mirror to eliminate the problem of coma. Since the mirror still is responsible for focusing the light, there is no chromatic aberration. Because of this catadioptric telescopes are popular among amateur astronomers. There are two basic types of catadioptirc telescope, the Schmidt and the Maksutov.

Catadioptric telescopes combine the best qualities of both refracting and reflecting telescopes and have few of their problems. In terms of price per unit aperture, Catadioptric telescopes tend to fall between refractors and reflectors. This is due to the fact that the corrector plate has to be ground.

Like reflecting telescopes, catadioptric telescopes also have a secondary mirror and hence a central obstruction. This also causes diffraction, though the corrector plate supports the mirror and there is no diffraction pattern caused by a mirror support.

1. Astronomy formulas, http://www.xmission.com/~alanne/AstronomyFormulas.html