Lenses and Waves

1655-1672 - DE ABERRATIONE 75
Huygens examined the means to enhance the quality of images produced by
telescopes with a convex ocular. That is, he took a theoretical look at the
matter. On the basis of this analysis, he could provide directions for
optimizing the quality of telescopes with convex oculars.
The magnifying power of a telescope depends upon the ratio of the focal
distances of objective and ocular lenses, and can therefore be increased by
reducing the focal distance of the ocular lens. This, however, simultaneously
decreases the clarity and distinctness of images. To maintain clarity at the
same time, the opening of the objective lens would have to be made larger. 97
He began by considering a naked eye in front of which a telescope is placed.
Assuming that an equal number of rays should enter the eye when a more
powerful telescope is taken, Huygens argued that the opening should be kept
proportional to the magnification. This implied that his 22-foot telescope
would need an opening of 125 times the area of the pupil. In reality, he
observed, a satisfactory telescope had a much smaller opening, only 15 times
the area of the pupil. Evidently, in astronomical observation one could do
with much smaller clarity. He therefore did not take the eye as starting-point,
but a telescope with satisfactory quality. If the ocular is replaced by an ocular
that magnifies twice as much, the clarity will be four times smaller. The
opening of the objective should therefore be increased accordingly.
Evidently, this cannot be done at will and one should “consider accurately
which magnification the opening of the exterior lens can support”. 98
Maintaining the clarity of images does not mean,
however, that their quality is maintained. Increasing the
opening of a lens renders images less distinct. Huygens
made it clear that only experience could tell which
configuration produced satisfactory images. Yet, when such
a telescope is known, theory can explain how the quality of
images is maintained when its strength increases. In his
account, Huygens applied a new conception of spherical
aberration that he had defined in an earlier proposition of
De Aberratione. He called it the ‘circle of aberration’. As
contrasted to the earlier conception, in which the aberration
GD is measured along the axis, the circle of aberration is
measured by the distance ED perpendicular to the axis
(Figure 30). In other words, the circle of aberration is the
spot produced by parallel rays coming from one point of a
distant object. Consequently, the images produced by two
lens systems are equally clear and equally distinct when the
respective circles of aberration are the same. 99
Figure 30 ‘Circle’
of aberration.
97
OC13, 332-335.
98
OC13, 336-337. “sed diligenter expendendum quale incrementum exterioris lentis apertura perferre
valeat”
99
OC13, 340-343.