Astronomy Principles and Practice Fourth Edition.pdf

Refractors 249
Figure 16.11. A beam of parallel light is brought to a focus by a double-convex lens (r is positive and r 2 is
negative).
Thus, by considering Rayleigh’s criterion in relation to equation (16.13), it should be possible to
resolve two stars if they are separated by an angle (in radians) greater than
α = 1·22λ
D . (16.14)
This value is known as the theoretical angular resolving power of the telescope. The physical
separation of the resolving power in the focal plane can be obtained by multiplying the value of α
from equation (16.14) by the focal length of the telescope. It can be seen that the resolving power
is inversely proportional to the diameter of the objective. By taking a value of 5500 Åasbeingthe
effective wavelength for visual observations, the resolving power can be expressed in seconds of arc as
α ≈ 140
D
(16.15)
where D is expressed in mm.
In summary, the ability of a telescope to resolve structure in a celestial object simply depends
on the ratio λ/D. The angle that can be resolved grows smaller according to the diameter, D, ofthe
telescope. It may be noted too (section 16.3.1) that the S/N ratio of any point image photometry also
improves according to the linear size of the telescope aperture.
We can now look at the main types of telescope system with particular reference to their ability to
collect light and produce good primary images.
16.5 Refractors
16.5.1 Objectives
The lens-maker’s formula expresses the focal length, F, of a lens in terms of the refractive index, n,
of the material (usually glass) and the radii of curvature, r 1 , r 2 , of the two lens’ surfaces. It can be
expressed conveniently in the form
(
1
1
F = (n − 1) − 1 )
. (16.16)
r 1 r 2
(In this form, values of r are positive when light rays meet a convex curvature and are negative when
they meet a concave curvature.) Thus, in general, if r 1 is positive and r 2 is negative, a simple lens
has a positive, real focus. A beam of parallel light which falls on the lens is, therefore, brought to
a focus as shown in figure 16.11. By applying this lens to a beam of light from a star which can be
considered to be at infinity, an image of the star will be formed at the focus of the lens. This image is
available for viewing with an eyepiece or for recording on a detector. The lens acts as light-collector
and image-former. When it is used in this way in a telescope system it is commonly known as the
objective.