Lenses and Waves

80 CHAPTER 3
A new design
We could have passed over this episode with Nulandt, if its conclusion had
not coincided with the next phase in Huygens’ study of spherical aberration.
On that same 1st of February, he gloriously
wrote down “A composite lens emulating a
hyperbolic lens. EUPHKA” 123 He had found a
new solution to the problem of neutralizing
spherical aberration that made his earlier one
superfluous. It consisted of a combination of
two lenses that would replace one objective
lens. This composite lens could therefore be
used in telescopes for astronomical
observation, whereas the earlier solution was
useful for terrestrial telescopes only. On
February 22, he asked his brother Lodewijk to
tell Constantijn
“… that I abandon the little ocular I had asked
from him, because I have found something better
and more substantial in these matters, that I would
like to try out myself.” 124
Huygens’ idea was as follows (Figure 33).
The bi-concave lens VBC and the plano-convex
lens KSTG have the same focus E, with respect
to diverging rays MV coming from M, and
parallel rays QK, respectively. In addition, the
spherical aberration EN produced by each lens
is the same for these rays. An arbitrary ray QK,
parallel to the axis ASM, is refracted by lens KST
towards point N, a little off its focus E. Lens
VBC, in its turn, refracts a ray MV towards the
same point N, at the same distance from its
focus E. Ray CN is therefore refracted towards
M. As a result, the composite lens brings all
parallel rays QK to a perfect focus M and “…
will emulate a hyperbolical or elliptical lens
perfectly.” 125 The system acts as a converging
lens and can therefore replace the objective of
any telescope. In his proof, Huygens worked
Figure 33 The invention of 1669
123
OC13, 408. “Lens composita hyperbolicae aemula. EUPHKA 1 Febr. 1669.”
124
OC6, 377. “Vous pourrez luy dire que je le quite pour ce qui est du petit oculaire que je luy avois
demandè, ayant trouvè quelque chose meilleur et de plus considerable en cette matiere, dont j’ay envie de
faire moy mesme l’essay.”
125
OC13, 413. “…[lens] compositae ex duabus VBC, KST, quae Hyperbolicae aut Ellipticae perfectionem
aemulabitur.”