Astronomy Principles and Practice Fourth Edition.pdf

274 Visual use of telescopes
By substituting for v in equation (17.2) and u in equation (17.3),
α e =
hF c
F e (F c + F e )
and
h
α c = .
F c + F e
Hence, the magnifying power of the telescope is given by
m = α e
= F c
(17.4)
α c F e
which is the ratio of the focal length of the collector to that of the eyepiece. Thus, in order to alter the
magnifying power of the system, it is only necessary to change the eyepiece for another of a different
focal length.
A further inspection of figure 17.2 shows that by considering the rays which enter the collector
parallel to the optic axis, the triangle formed by the diameter of the collector, D, and the primary image
at F is similar to the triangle given by the diameter of the exit pupil, d, at the distance of the eye lens,
and the primary image. Thus,
D
d = F c
= m. (17.5)
F e
An alternative way to express the magnifying power of a telescope is to evaluate the ratio of the
diameters of the collector (entrance pupil) and the exit pupil.
If an object subtends a certain angle to the unaided eye, the use of a telescope increases this angle
at the eye by a factor equal to the magnifying power. In some cases, detail within an object cannot be
seen by the naked eye, as the angles subtended by the various points within the object are too small to
be resolved by the eye. By using a telescope, these angles are magnified and may be made sufficiently
large so that they can be resolved by the eye at the eyepiece. A simple example of the use of the
magnifying power of the telescope occurs in the observation of double stars. Many stars which appear
to be single to the unaided eye are found to be double when viewed with the aid of a telescope. To
the naked eye, the angular separation of the stars is insufficient for them to be seen as separate stars.
By applying the magnification of the telescope, the angle between the stars is magnified and, in some
cases, it becomes possible to see the two stars as separate bodies.
17.2 Visual resolving power
As described in section 16.4, the angular resolving power of a telescope may be defined as the ability
of a telescope to allow distinction between objects which are separated by only a small angle. For the
case of a telescope used visually, the theoretical resolving power based on Rayleigh’s criterion may be
written as (see equation (16.15))
α ≈ 140
(17.6)
D
where α is in arc seconds when D is expressed in mm.
A skilled observer, however, can resolve stars which are, in fact, closer than the theoretical
resolving power. In other words, the observer is able to detect a drop in intensity at the centre of
the combined image which is less than 20% (see figure 16.10). In other words, if the observer is able
to detect a dip in intensity smaller than 20% in a dumbbell-like image, then the two stars have been
resolved at an angular separation smaller than the Rayleigh criterion. Other more practical criteria
for resolving power have been proposed according to particular observers’ experiences. The Dawes’