University Lowbrow Astronomers

What Do Telescopes Do?

by Doug Scobel
Printed in Reflections: July, 2003.

Sounds like a simple enough question, doesn’t it?  But the answer isn’t as simple as you might think.  The telescope must perform a number of functions all at once, and all these functions are interrelated.

BASIC FUNCTIONS OF THE TELESCOPE

Since most if not all of you already know this, I’ll just touch on them lightly.  There are three basic functions of a telescope (at least those used by most amateurs) - light gathering, resolving, and magnifying.

Light gathering power is a measure of how much light the objective (primary mirror in a reflector, lens in a refractor) can collect from distant objects.  Nominally, it is proportional to the square of the diameter of the aperture.  Doubling the aperture results in gathering four times as much light.

Resolving power is a measure of the amount of detail that is possible to see in the image.  Nominally, it is proportional to the diameter of the aperture.  Doubling the aperture results in resolving details that are half the size, ideally, at least.

Magnification is not an inherent property of the telescope, but rather something that the telescope must be made to do to be able to see anything through it.  In other words, the image produced by the telescope’s optical train must be made large enough so that you can see details in it.  As we’ll see later, there are upper and lower limits to how much magnification you should use visually.

WHAT’S MORE IMPORTANT, MAGNIFICATION OR APERTURE?

Many believe that magnification is the most important factor in a telescope.  Well, this is partially true, because a telescope that does not magnify is pretty useless (single power reflex type finders notwithstanding).  But, too much magnification causes a host of problems in the image.  A partial list of these problems is:

  1. The image becomes too dim, because the light is spread out over a too large area.
  2. Optical train aberrations become overly noticeable.
  3. Atmospheric effects become objectionable.
  4. Vibrations and/or instability in the mounting prevent the image from staying in one place.
  5. The image can be magnified to the point where it is no longer useful.

Others believe that simple aperture is what’s important, the more the better.  Well this is also only partially true, because a telescope that does not collect more light than your unaided eyes is just as useless as one that does not magnify.  But, too much aperture (some believe this to be an oxymoron!) also can cause problems, such as:

  1. Weight and bulk of the telescope can become excessive, making it less or not portable.
  2. Height of the eyepiece (in Newtonian reflectors) when pointing near the zenith can require climbing a tall ladder, in the dark, potentially on uneven ground, when you’re tired, etc.
  3. Tube length (in refractors) becomes so long as to become nearly impossible to mount effectively.
  4. The telescope becomes overly expensive.

Often, a telescope that is too large and difficult to transport and/or set up and/or use will tend not to be used much.

There obviously needs to be some kind of happy medium, where the aperture and magnification are balanced and work with, instead of against, each other.  In fact, the two depend on each other.

MAGNIFICATION

Magnification in a telescope is determined by the simple expression:

Magnification = Effective Focal Length of the Telescope / Focal Length of the Eyepiece

In virtually all telescopes, the focal length remains fixed, so you vary the magnification by using eyepieces with different focal lengths.

EXIT PUPIL

Before we go on, we need to talk about the exit pupil.  The exit pupil is what we call the small disk of light coming out of the eyepiece.  If you put an eyepiece into the focuser and then stand back a ways, you’ll see a small circle that appears be suspended in space a little way back (towards you) from the eyepiece.  This distance from the eye lens of the eyepiece to the exit pupil is known as the eyepiece’s eye relief.  The exit pupil is actually an image of the telescope’s objective, and if the telescope is an obstructed reflector, then you’ll see the silhouette of the secondary in the center as well.  For optimal viewing, you must place your eye such that your eye’s pupil is coincident with the telescope’s exit pupil.

The diameter of the exit pupil is dependent on the aperture and the magnification, in particular:

Exit pupil diameter = Aperture / Magnification

Lower magnifications produce a larger exit pupil, and higher magnifications produce a smaller exit pupil.  As we’ll see later, the exit pupil diameter comes into play when choosing eyepieces, and can be critical when choosing a low power eyepiece.

HIGHEST USEFUL MAGNIFICATION

From a practical standpoint, there is a highest magnification you should use, for the reasons outlined above.  As a general rule of thumb, the upper limit is about 50x per inch of aperture.  But this is a generality - sometimes you can use more, sometimes you can’t go that high.  Just a few of the factors that can limit how much magnification you can use are poor atmospheric steadiness, poor optics, a shaky mount, difficulty getting an eyepiece with a short enough focal length or with enough eye relief, etc.

Because telescopes, observers, and observing conditions vary so much, it’s really up to the observer to decide when too much is too much.  It’s a self-correcting problem, though.  When adding magnification makes the image worse, rather than better, then you know that you’ve gone too far.

LOWEST USEFUL MAGNIFICATION

Conversely, there is a lowest magnification you should use, at least if you want to use the entire aperture of your telescope.  The idea is to match the diameter of the telescope’s exit pupil to that of the pupil of your dark-adapted eye.  For you youngsters out there, that’s about 7mm.  For older folks like me, it’s more like 6 or even 5 mm.  If you go with too little magnification, then the exit pupil becomes too large, and some of the light is blocked by your eye’s iris rather than entering the pupil.  It’s just like stopping your scope down to a smaller aperture.

The fortunate part is that it is easy to calculate the diameter of the exit pupil.  For example, an eight inch (203 mm) telescope at 30x will provide almost a 7 mm exit pupil.  So, your lowest power eyepiece should have a focal length to provide about 30x.  If you were to go lower, say to 20x, the exit pupil will be more than 10 mm in diameter, which is too large to fit into your eye.  Your eye’s pupil will then act as an aperture stop, effectively stopping your eight inch telescope down to under six inches in diameter!

It’s more convenient to express this optimal low power eyepiece (OLPE) in terms of its focal length, which happens to depend only on your telescope’s focal ratio.  The expression is:

OLPE Focal Length = Exit Pupil Diameter x Focal Ratio

For example, for all f/5 telescopes, and a desired exit pupil of 7 mm, the OLPE would have a 35 mm focal length.

So how do you know if your exit pupil is too big, since most people don’t know the diameter of their dark adapted eye’s pupil?  What you can do is put in your lowest power eyepiece, center a relatively bright star in the field (but not too bright, because your pupil may constrict a little), and then defocus the star’s image until you see a large disk.  If your exit pupil is too large, then you will see the outer edge of the expanded disk move around and change shape as you try to keep your head steady.  You will actually see how your eye’s iris is blocking some of the light.  But if the outline of the image seems to “stand still”, and remain circular, then you’re OK and all the light is entering your eye.

Now there is a time when it is valid to go with a “too low” magnification, and that is when you need that larger real field of view, say while scanning for some faint object like a comet.  Nothing bad will happen, just realize that you’re not using the full diameter of the objective when you do, and you are simply sacrificing image brightness for a larger actual field of view.  But once you’ve found your target, switch to your OLPE for the optimal low power view.

RESOLVING POWER

Resolving power can mean at least two things.  One is the amount of detail you can see in an extended object, say a planet.  Another is how well your telescope can split close double stars.  They are not necessarily the same measure.

To see the maximum amount of detail in a planet, top optical quality is essential, especially when the object’s detail has low contrast.  Good optics will concentrate as much light as possible into the center of the diffraction pattern, and scatter a minimal amount of light outside of it.  This not only requires good optics, but it also requires that those optics are clean, well aligned, with little or no thermal currents in the light path, shielded from stray light, on a steady mount, with a steady atmosphere, etc.

But, to resolve close doubles, top optical quality is not necessarily required.  In fact, you’ll be able to split slightly closer doubles with a telescope with a little less than perfect optics, than you can when your optics are perfect.  The reason is that with less than perfect optics, less light goes into the so-called Airy disk in the diffraction pattern, and more goes into the surrounding diffraction rings.  This makes the Airy disk appear smaller, and hence it is easier to discern whether there are two stars or one.  You can take this too far, though.  Too poor of optics cause the diffraction pattern to degrade to the point where the two star images kind of merge together.

WHAT IT ALL MEANS

In the end, the single most important factor in determining how well a telescope will perform is aperture.  The more aperture you have, the more light in the image, and the better the theoretical resolution in that image.  Now there are practical limits to how much aperture you can use in practice, but there’s too much to write about on that subject, so I think I’ll save that for another time.

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Copyright © 2013, the University Lowbrow Astronomers. (The University Lowbrow Astronomers are an amateur astronomy club based in Ann Arbor, Michigan).
This page originally appeared in Reflections of the University Lowbrow Astronomers (the club newsletter).
This page revised Sunday, March 9, 2014 4:30 PM.
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