Astronomy Principles and Practice Fourth Edition.pdf

276 Visual use of telescopes
17.3 Magnification limits
There are both lower and upper limits to the magnification which can be usefully applied with any
given telescope. The first consideration for a lower limit is that all the light which is collected by the
telescope should be made available for viewing by the eye; the magnification must be sufficiently great
to make the exit pupil equal to or smaller than the entrance pupil of the eye (see figure 17.2). Thus, by
using the definition of magnification given by equation (17.5), this condition can be written as
m ≥ D d
where d is the diameter of the pupil of the eye and D the diameter of the telescope aperture. Under
normal observing conditions, a typical value of d is 8 mm and, thus, the lower limit of magnification
is set by
m ≥ D (17.7)
8
where the diameter of the telescope is again expressed in mm. If the magnification is less than the value
given by equation (17.7), some light will be lost and the full collecting power of the telescope is not
being utilized. This consideration is very important, except perhaps when the Moon is being viewed.
A further lower limit to the magnification is set by the resolving power of the eye. If any detail in
a complex object is to be viewed, the angular size of its image must be larger than the eye’s resolving
power. This latter quantity depends, to a great extent, on the observer but a typical value can be
taken as one minute of arc. If a certain resolution has been achieved by using a particular telescope,
the magnification must have a value which is sufficient to allow the resolved details to be seen by eye.
Thus, by matching the resolution of the telescope (equation (17.6)) to that of the eye (≈ 60 arc seconds)
by means of magnification, a lower limit of magnification is set by
or
m ≥ 60D
140
m ≥ 3D 7 .
As the value taken for the resolving power of the eye favours an extremely good eye, the lower limit of
magnification can be conveniently approximated to
m ≥ D 2
(17.8)
where the diameter of the telescope, D, is again expressed in mm.
The useful magnification of a telescope cannot be increased indefinitely. The upper limit is set by
the impracticability of making eyepieces with extremely short focal lengths, by the quality of the optics
of the collector and by the fact that the ability of the eye to record good images deteriorates when the
beam that it accepts becomes too small. For the image to be seen without loss in the quality of the
eye’s function, the exit pupil must be larger than 0·8 mm. By using equation (17.5) for the expression
defining magnification,
m ≤ D
(17.9)
0·8
where, again, the diameter of the telescope is in mm. Comparison of equations (17.7) and (17.9) shows
that from a consideration of the size of exit pupil, the magnifying power of any telescope has a useful
range covered by a factor of ten.