QUESTION:
What is meant by the phrase 'the power of a telescope'?

ANSWER from Scott Sandford on May 20:
This question actually has several answers since different 
people mean different things when they talk about the 'power' of a 
telescope.

One of the more common meanings for the word 'power' when used with 
telescopes is as a measure of the angular magnification produced by the 
telescope.  By angular magnification, I mean that the object looks bigger (it 
takes up a bigger angular part of your field of view) when you look at it 
through the telescope.  So, if an object looks twice as big through a 
telescope as it does with your naked eye, you would say the telescope has a 
magnification power of 2.  The magnifying power of a telescope depends on the 
lenses or mirrors it contains.  For a refracting telescope, the angular 
magnification is equal to the focal length of the objective lens (the big lens 
in the front) and the focal length of the eyepiece lens.  So, if a telescope 
had an objective lens with a focal length of 240 cm and uses an eyepiece that 
has a focal length of 2 cm, it would have a magnification of M = 240/2 = 120.  

If you wanted a higher magnification, you could change the eyepiece to one 
having a shorter focal length.  For example, if you put in a new eyepiece 
with a focal length of 1 cm, the magnification would increase to M = 240/1 
= 240.  Most small telescopes come with several lenses so you can change 
the magnification to suit the situation.  There is a practical limit to how 
high you can go in magnification for any given telescope, however.  Eventually 
you reach a point where higher magnifications give you bigger images but 
you find you can't focus the telescope to get a sharp picture, i.e. you reach a 
point where you get larger but fuzzier images.  At this point there is really 
no value in using higher magnifications.

The word 'power' is also used with telescopes to describe the telescope's 
ability to collect light.  The bigger a telescope is in diameter, the more 
light passes down it, and the more light ends up at the eyepiece.  This makes 
the object you are looking at appear brighter.  This explains why you can see 
some stars through binoculars or small telescopes that you can't see with 
your naked eye.  Binoculars and telescopes have bigger diameters than your 
eyes, so they collect more light and make everything look brighter.  Stars 
that were too dim to see before become visible.  The amount of light a 
telescope collects can then be thought of as its 'light gathering power.'

These two types of telescope 'power' are independent of each other, that is, 
you can have any combination of the two - telescopes that gather a lot of 
light but don't have a very high magnification, ones that gather a lot of light 
and do have a very high magnification, telescopes that gather very little light 
but have a high magnification, and telescopes that gather little light and 
don't have a very high magnification either.

The telescope an astronomer will chose to use will depend on the type of 
study he or she is trying to complete.  Most of the astronomy I do is in the 
field of spectroscopy, which is basically the measurement of the colors of 
things.  Normally when you are doing spectroscopy you want as much light 
as you can get, but you often don't care much about the magnification.  In 
this case a big telescope is important, but high magnification isn't very 
critical.  However, suppose I wanted to measure the color of a star that is 
part of binary star system, i.e. a star that is orbiting closely about another 
star?  In that case, I would want a big telescope (so I could collect a lot of 
light for my color measurement), but I'd also want a telescope with high 
magnification (so I could separate the two stars from each other, otherwise 
I'd be measuring the color of both stars together, rather than just the one I 
was interested in).

I hope this helps!

Scott Sandford
Astrophysics Branch
NASA-Ames Research Center