Desirable characteristics of telescopes

1. Size of light collector. The light gathered is proportional to the area of the objective and (see below) the resolution is proportional to the diameter of the objective lens or mirror.

2. Magnification. Magnification only matters for optical telescopes. It is defined to be (angular size with instrument)/(angular size without instrument). That is the same as (focal length of objective)/(focal length of eyepiece). It is easily changed by choosing a different eyepiece; the useful magnification is limited by the objective diameter. (If you magnify a blur, you just see a big blur).

3. Resolving power, or resolution. This is the ability to discriminate between two different objects which are very close to each other. It is defined to be the number of degrees (or minutes or seconds) of arc which separate two barely distinguishable objects.

   For example, suppose there are two lights, one foot apart, and 5000 feet away. Suppose further that when they are viewed through a telescope, they can be seen as two, but if they were any closer to each other, they would appear to be one single object. Their angular separation is the same fraction of a circle as their 'linear' separation ( one foot) is of the 'linear' size of the circle they're on (two pi times 5000 feet).

   

   
   
   

   Therefore the resolving power of that telescope is

   R.P.=(360^o) times $${\frac{1 \textrm{ft}}{2\pi(5000 \textrm{ft)}}}$$, which is about .01 degree. One sixtieth of a degree is one ``minute'' of arc, so a hundredth of a degree is about 1/2 minute.

   What is there about a particular telescope that decides what its resolving power will be? Two things: the diameter of objective lens or mirror and the wavelength of the radiation being detected. The larger the diameter, the better the resolving power; the smaller the wavelength, the better the resolving power. The formula is, approximately, (wavelength/diameter), or $\lambda$/d. For example, radio telescopes must be much bigger (across) if they are to have resolving power as good as optical telescopes, since $\lambda_{optical}^{}$ > > $\lambda_{radio}^{}$.

   The resolving power of the human eye is about 10 seconds of arc, or 10 arcseconds, or, simply, 10 seconds.

   The resolving power of the 200'' telescope is about .02 sec. (The Hale telescope at Palomar mountain in California, long (but no longer) the largest in the world, was called the ``two hundred inch telescope'' for the first thirty or so years of its life; in these metric times it's called the ``five meter.'')

   The resolving power of a large radio telescope is about 100 sec.

   The resolving power of two large radio telescopes, separated by thousands of miles but used as a single instrument (called ``intercontinental interferometry'') is as good as or better than that of the largest optical telescopes.

   Earth based optical telescopes rarely achieve such resolving power: atmospheric turbulence degrades it. Telescopes 'in space' (outside the earth's atmosphere) routinely do so.