Lenses and Waves

1690 - TRAITÉ DE LA LUMIÈRE 217
the limited quality of telescope images. He now realized that the effect of
spherical aberration was small as compared to the aberration “… that arises
from the Newtonian dispersion of rays.” 11 He set out to make a new table of
optimal configurations, which would also take the ‘Newtonian’ aberration
into account. 12
Huygens explained the difficulty with telescopes in the same way he had
done in 1665: increasing the magnification renders images fuzzy and
obscure. 13 The problem was how to increase the power of a telescope whilst
maintaining the clarity and distinctness of images. This came down to
determining the aperture of the objective lens in proportion to the aperture
of a given telescope of good optical qualities. 14 Huygens first determined the
amount of chromatic aberration of a lens relative to its focal distance. He
more or less repeated what he had written to Newton in 1672. Huygens had
argued that the ratio between the aberration and the focal distance was
1 : 25, whereas Newton had used 1 : 50. 15 This meant that chromatic
aberration exceeded spherical aberration 39 times and would imply that it
was superfluous to take spherical aberration into account when dealing with
the quality of images. 16 Huygens explained that in reality things were not as
bad as these figures suggested. Repeating further arguments from his dispute
with Newton, he said that many of the dispersed rays were not perceptible.
Therefore lenses did produce images that were sufficiently distinct, although
they might be surrounded by a faint ‘nebula’. 17
First, Huygens considered the chromatic aberration NM, produced on the
retina by a telescope consisting of two convex lenses AC and DP (Figure 78).
The axis of the system is TPC, F is the focus of the red rays refracted by the
objective lens AC and B the focus of the violet rays. In this type of telescope
the foci of objective and ocular lens should coincide, but the focal distances
of the various colors differ. Huygens assumed the foci of the red rays to
coincide. F is also the focus of the red rays for the ocular PD, G is the focus
of the violet rays. Consequently, red rays will be refracted along AFO,
towards LK parallel to the axis, and point N, where the axis intersects with
the retina. Next, Huygens considered the path of the violet rays. These are
refracted by the objective lens towards ABD. As G is the focus of the violet
rays for the ocular, a ray GD will be refracted towards DE and N on the
retina. Ray ABD is not refracted towards DE, however, but towards DK and
thus reaches the retina in M. Consequently NM is the aberration produced by
the system. Because – by a small angle approximation – angle NKM is equal
11
OC13, 621. “… ex dispersione radij Newtoniana.”
12
OC13, 496-499.
13
OC13, 480.
14
OC13, 482. Compare section 3.2.1 on De aberratione below.
15
OC13, 484-487 and 485 note 8. The manuscript is confusing as Huygens first derived his own figure of
1 : 25 but used Newton’s figure of 1 : 50 when he later inserted the numbers into the text.
16
According to his own figure of 1 : 25 this should be 79.
17 OC13, 486-487.