Chapter 2 - How Telescopes Do What They Do

Jack Kramer

1. Magnification

The job of a primary mirror or lens is to gather as much light as possible (to provide as bright an image as possible), to magnify the image, and present it to the eyepiece, which further magnifies the image. Those who are brand new to astronomy invariably judge a telescope by how much it magnifies - its power - denoted by the letter "x". Many scopes sold in department stores are advertised with magnifications as high as 300x, or even 400x. But just try to use those magnifications! In reality, there's a maximum usable power of about 50x per inch of aperture under perfect observing conditions (which are very rare). This means that a 60mm refractor (2.4") has a maximum usable magnification of 120x. With anything greater than that, the field of view will be too small to hold the image steadily and the image itself will simply be a fuzzy, indistinct blob. After a certain point, magnification simply spreads out the incoming light particles into an indistinct, useless blur. Add to this the typical atmospheric conditions and you can appreciate that 50x per inch is optimistic. Experienced amateur astronomers typically use magnifications in the range of 10x to 20x per inch of aperture, and often a lot lower magnification than that. A telescope should be judged by its light grasp, and that's a function of the diameter of the objective lens or mirror.

When speaking of telescope characteristics, we generally refer to dimensions in millimeters. The conversion from inches is simple; one inch equals 25.4 millimeters. To determine what magnification (X) a telescope will yield with a particular eyepiece (or "ocular"), divide the focal length of the telescope (Ft) by the focal length of the eyepiece (Fe):

X = Ft / Fe.

Plugging some numbers into the preceding formula, we see that a telescope of 1250mm focal length using an eyepiece of 12.5mm focal length would produce a magnification of 100x.

2. Field of View

One reason why it's more difficult to see things under high magnification is that the field of view becomes smaller as you go up in power. The image becomes larger, so the existing light is spread out over a larger area and the image is dimmer. (That's another reason why the view isn't as good.) The field of view in its simplest form refers to how much of the sky you can see through the telescope. But the field of view doesn't depend solely on the magnification. Different eyepiece designs have different fields of view. Generally, those with wider fields are more expensive because larger eyepiece lenses are required and more of them are required in order to take that little cone of incoming light and keep it sharp, while making the best use of the field of view presented by the telescope. The following CCD images of M13 in Hercules give some inkling of the difference between the wide field and narrow field eyepieces. The magnification is identical in both views.

Field of View

Actual Field of view refers to the actual degrees of sky that your eye takes in when looking through the eyepiece. There are three fairly easy ways to determine this field of view:

a) Find two bright stars in the sky that are at the extreme opposite edges of your field. Then check on a star chart to determine how many degrees apart they actually lie.

b) Aim your scope at a star withing 10o of the celestial equator and center it in the eyepiece. Then time how long it takes for the star to drift from the center to the edge. The number of seconds divided by two equals the field diameter in arc minutes.

c) Another method is to calculate it by dividing the apparent field of view for that eyepiece by the power yielded from the eyepiece in your telescope. (Eyepiece suppliers usually state that certain eyepiece designs yield certain "apparent" fields of view.) So the formula is as follows:

ActualFOV = AppFOV / X.

As an example, let's say you have an Orthoscopic design eyepiece that gives 65x in your telescope. Since the apparent field in most Orthoscopics is 45o, the actual field of view ends up about .7o , or about three quarters of a degree (45 divided by 65).

Apparent field of view is how much sky it looks like you're seeing; it's dependent entirely on the eyepiece used. An eyepiece with a narrow field of view makes it appear as though you're looking at the sky through a tube. A wide field makes it seem as though you're looking at the sky through a porthole. Obviously, the view will be more pleasant with a wider field of view. Here are the apparent fields of view generally provided by some of the more common eyepiece designs:

Eyepiece Apparent FOV
Kellner 40
Orthoscopic 45
Plossl 50
Konig 55
Erfle 60
Tele Vue Wide Field 65
University Wide Scan 70-80
Nagler & Meade Ultra Wide Angle 82

A word of advice is in order about the eyepieces included with the cheaper telescopes - primarily those sold in department stores. They normally come with eyepieces of the Huygenian or Modified Achromat design. Both of these are antiquated designs that produce narrow fields of view with some distortion at the edges of the field. On top of that, the lenses in these inexpensive eyepieces are often of inferior quality. In fact, it's not uncommon for the manufacturers of cheap telescopes to use plastic, instead of glass lenses. If you have a typical 60mm "department store" refractor, one of the easy and effective upgrades you can make is to purchase new eyepieces of the Kellner or Orthoscopic design. You'll be amazed what a difference that can make. The eyepiece barrel size generally used on these telescopes is .965". An even better alternative would be to buy or make an adapter so you can use the more common 11/4" eyepieces. This greatly expands your ability to use the better eyepiece designs. The adapter may move your eyepiece a bit farther out from the incoming cone of light, so make sure your focuser provides enough in-focus travel to still bring images into sharp view.

3. Focal Ratio

The field of view also depends on the focal ratio of the telescope. Focal Ratio is simply the ratio of the focal length to the diameter of the lens or mirror. For example, a telescope with a 10" mirror having a focal length of 56" would have a focal ratio of 5.6 - the focal length is 5.6 times the diameter of the mirror and is denoted as f/5.6. (Notice that as the size of the optics gets larger, we usually revert to using inches instead of millimeters; but eyepiece sizes are always stated in terms of millimeters.) Lower focal ratios yield wider fields of view and are referred-to as "fast" systems. Telescopes with higher focal ratios have longer focal lengths, produce higher magnification, but with a narrower field of view. Observers who are particularly interested in the deep sky - galaxies, star clusters, and nebulae - prefer a telescope that gives a nice wide field of view. On the other hand, if your interest is planets, then field of view isn't as important as magnification and sharpness of detail. An optical system with a long focal length does not "bend" the light rays at such a steep angle as does a fast system, so it's more forgiving in terms of optical quality and generally provides a somewhat sharper image. Of course, a higher focal ratio results in the telescope tube being longer in order to accommodate the longer focal length. You will notice that most refractors have higher focal ratios, while reflecting telescopes have lower ratios. One reason for this is purely practical. Take the example of our 10" reflecting telescope. If it had a focal ratio of f/10, that would give it a focal length of 100", and the telescope would have a tube about 8 feet long. That's pretty unwieldy!

f/1 focal ratio

f/1 Focal Ratio

f/6 focal ratio

f/6 Focal Ratio

4. Image Orientation

Astronomical telescopes do strange things to the images, depending on the number of times the light is reflected before it gets to the eyepiece:

a) An equal number of reflections turns the image upside down (as in a Newtonian)

b) An odd number of reflections turns the image left to right (as in a Schmidt-Cassegrain or a refractor with diagonal)

This really doesn't matter too much because in space there's no such thing as "up or down". However, the confusion comes when you move the telescope and watch as the images in the eyepiece go in a different direction than you expected. The other problem is that you have to understand the orientation of the image when checking it against a star chart. As you become an experienced observer, you soon become accustomed to these quirks. Incidentally, this image orientation prompts many observers to prefer a straight-through finder telescope, rather than one with a diagonal. A straight-through finder, like any refractor without a mirror to redirect the light, presents a correct ("normal" up-down, right-left) image.

Standard Accessories

Two accessories are important on an astronomical telescope: a finder and a right-angle adapter (or "diagonal"). The finder is a small telescope mounted on the tube of the main telescope and exactly aligned with it. The finder is a low-power, wide-field scope that allows you to more easily locate objects in the sky so that they'll be in the higher-power, narrower-field view of the main telescope. The best finders are at least 6x30 (6 power by 30 mm in diameter); with anything smaller, you might as well be using a soda straw! You'll have to check the finder regularly and realign it as necessary. They're held by set screws and tend to get out of alignment from the normal vibrations of hauling around the telescope. If you have a refractor or Schmidt-Cassegrain, a diagonal allows you to look at objects high overhead without breaking your neck or having to lie on the ground to look into the eyepiece. Make sure the diagonal bends the light 90o. There are some diagonals that provide an erect image for terrestrial viewing, but bend the light only 45o; these are almost as awkward as no diagonal at all.


5. Unique Aspects of a Newtonian Reflector

The following cutaway view shows the distance relationships between the various components of a Newtonian reflector. These formulae have proved to be reliable for the average telescope. Even if you never take apart your Newtonian, it's good to understand how the components go together - this will provide a better grasp of issues related to collimation, focal ratios, and eyepiece selection.


As noted before, the relatively low cost of the Newtonian telescope allows you to purchase one with larger optics. Remember that the larger the primary mirror, the more light gathering power you have. Therefore, you will have maximized your instrument dollars.

The Mirror Cell

The mirror cell is the apparatus that holds the primary mirror at the base of the telescope tube and allows you to collimate the optics. To "collimate" simply means to ensure that the primary and secondary mirrors line up with each other; we'll discuss this in more detail a little farther on. The mirror cell has to allow you to tilt the primary mirror as needed to bring the components into alignment. The example shown here is typical of homemade cells which can be made quite easily out of wood, springs and screws. However, it's also quite similar to cells that are used on commercially-made telescopes. The most important thing is that the mirror be held firmly in place, but not so tightly as to cause the Pyrex mirror to become deformed. This deformation would be so slight that you'd never notice it by looking at the mirror, but it would change the figure of the mirror and adversely affect the images. (You'll notice a similar phenomenon whenever you take a Newtonian reflector out of the house to observe on a cold night. The change in temperature causes the mirror to flex very slightly and it will take at least a half hour before the mirror reaches ambient temperature and the images can be focused sharply.)