Astronomy Principles and Practice Fourth Edition.pdf

Comparison of refractors and reflectors 269
Figure 16.32. Example 16.2—circle of least confusion of a chromatic change.
size increases. The mechanical strains, due to the collector’s own weight, will vary according to the
point in the sky to which the telescope is directed; for large telescopes the strains are sufficient to
distort the optical surfaces and spoil the images. Very little can be done in the case of the refractor as
the objective can be supported only by its rim. However, in the case of a reflector, the collector can be
supported over all of the rear surface. In fact, it is possible to design a system of pressure pads in the
support to relieve the strain in the mirror, according to its position.
From the point of view of light-gathering power, it is not profitable to construct large refractors.
As the diameter of the objective increases, so does its thickness and the amount of absorption. The ratio
of the transmission to the diameter decreases as the telescope aperture increases and, thus, the law of
diminishing returns applies. For reflectors with the same focal ratio but ranging in size, the fractional
loss in transmission efficiency is constant. Other properties of telescope systems are discussed later in
their relevant sections. Those which can be compared have been summarized in table 16.1.
Example 16.2. A 400 cm diameter lens has focal lengths in the blue and red regions of the spectrum
given by: F B = 2995 mm, F R = 3000 mm.
(i) What is the value of the focal length corresponding to the position of the circle of least
confusion
(ii) What is the linear size of the image of a star at its focal position
(i) By similar triangles (see figure 16.32):
D
F B
=
d
F c − F B
and
D
F R
=
d
F R − F c
.
Dividing these identities,
giving
Inserting the values gives
F R
F B
= F R − F c
F c − F B
F c =
2F B F R
F R + F B
.
2 × 3000 × 2995
F c =
5995
F c = 2997 mm.