Fundamental Astronomy

Fig. 3.6a–e. Diffraction and resolving power. The image of
a single star (a) consists of concentric diffraction rings, which
can be displayed as a mountain diagram (b). Wide pairs
of stars can be easily resolved (c). For resolving close bi-
In night vision (when the eye is perfectly adapted to
darkness) the resolving capability of the human eye is
about 2 ′ .
The maximum magnification ωmax is the largest magnification
that is worth using in telescopic observations.
Its value is obtained from the ratio of the resolving
capability of the eye, e ≈ 2 ′ = 5.8 × 10−4 rad, to the
resolving power of the telescope, θ,
ωmax = e/θ ≈ eD/λ = 5.8 × 10−4 D
5.5 × 10−7 m (3.5)
≈ D/1mm.
If we use, for example, an objective with a diameter of
100 mm, the maximum magnification is about 100. The
eye has no use for larger magnifications.
The minimum magnification ωmin is the smallest
magnification that is useful in visual observations. Its
value is obtained from the condition that the diameter
of the exit pupil L of the telescope must be smaller than
or equal to the pupil of the eye.
The exit pupil is the image of the objective lens,
formed by the eyepiece, through which the light from
3.2 Optical Telescopes
naries, different criteria can be used. One is the Rayleigh
limit 1.22 λ/D (d). In practice, the resolution can be written
λ/D, which is near the Dawes limit (e). (Photo (a) Sky
and Telescope)
the objective goes behind the eyepiece. From Fig. 3.7
we obtain
′ f D
L = D = . (3.6)
f ω
Thus the condition L ≤ d means that
ω ≥ D/d . (3.7)
In the night, the diameter of the pupil of the human eye
is about 6 mm, and thus the minimum magnification of
a 100 mm telescope is about 17.
Fig. 3.7. The exit pupil L is the image of the objective lens
formed by the eyepiece
51