Astronomy Principles and Practice Fourth Edition.pdf

250 The optics of telescope collectors
Figure 16.12. The dispersion curve of a typical crown glass.
A single-lens objective is unsatisfactory for astronomical purposes as the images produced suffer
from defects or aberrations of different kinds. Considerable effort has been applied to the design of
objectives to remove or reduce the aberrations and refractor telescopes show a variety of construction
depending on their intended function and the way particular aberrations have been compensated.
Telescope objectives may suffer from the following defects:
(i) chromatic aberration,
(ii) spherical aberration,
(iii) coma,
(iv) astigmatism,
(v) curvature of field,
(vi) distortion of field,
and each of these effects is discussed in the following subsections.
16.5.2 Chromatic aberration
A closer look at the lens-maker’s formula (equation (16.16)) reveals why the image produced by a
single lens suffers from chromatic aberration. For a given lens of known shape, the lens-maker’s
formula may be re-written so that the focal length may be expressed by
F =
K
(n − 1)
(16.17)
where K = r 1 r 2 /(r 2 − r 1 ). (For a positive lens, K is also positive.)
The term (n − 1) is known as the refractive power of the material of the lens.
The refractive index and, hence, refractive power of all common materials used for lenses
exhibits dispersion, i.e. its value is wavelength-dependent. A typical dispersion curve is illustrated in
figure 16.12 and it depicts the fact that the refractive index progressively decreases as the wavelength
of the light increases. Thus, the focal length of a single lens depends on the wavelength of light that
is used and, for a simple positive lens, the focal length increases as the wavelength increases. If,
therefore, a single positive lens is illuminated by a parallel beam of white light, a spread of images is
produced along the optic axis of the lens. This is illustrated in figure 16.13. At no point along the optic
axis is there a position where a point image can be seen: at the position where an image is formed for
the extreme blue end of the spectrum, this image is surrounded by a red halo; similarly at the position
where an image is formed for the extreme red end of the spectrum, this image is surrounded by a blue
halo. Between these extreme positions, there is a plane which contains the smallest possible image