Lenses and Waves

66 CHAPTER 3
“We give here, if not the best combination of all lenses, the investigation of which
would take long and might be impossible, but one which experience has shown us to be
useful.” 58
The particular configuration of Huygens’ eyepiece was a product of trial-anderror,
and theory could not, or not yet, add to that. Huygens the scholar had
not yet been able to assist Huygens the craftsman.
As contrasted to other telescope makers, however, Huygens was able to
understand retrospectively and in mathematical terms, what he was doing
when configuring lenses. That is to say, he understood the dioptrical
properties of lenses and their configurations. He could explain whether and
how a configuration of lenses produced sharp, magnified images. But he
could not explain everything of the kind. In another proposition found in
part III of Tractatus and apparently following the one discussed above,
Huygens discussed a telescope with an erector-lens such as Kepler had
proposed. 59 He concluded with some remarks about the quality of images
produced by various configurations. With a telescope consisting of a convex
objective and a concave ocular – the Galilean configuration – images are
more distinct “and defiled by no colored rims that can hardly be prevented
in this composed of three lenses.” 60 A well-chosen combination of lenses
could counter these defects, but
“different people combine ocular lenses differently with regard to each other, looking
for the best combination with only the guide of experience. It would not be easy, to be
sure, to teach something about this that is grounded in certainty, since the consideration of
colors cannot be reduced to the laws of geometry, ….” 61 [italics added]
In his practical work Huygens had found out that lenses suffered from all
kinds of defects. Some of these eluded dioptrical analysis. But he had also
found out that nuisances caused by fogs, bubbles and colors could be
diminished. The diaphragm had already proven this. His eyepiece gave
another means to improve the quality of images. 62 He could not fully explain
its advantages, nor could he improve it by means of dioptrical analysis. Still,
the eyepiece had proven that a well-chosen configuration of lenses could be
advantageous. And it made him realize that even better configurations could
be found, even though he was as yet pessimistic about such an enterprise. If
Huygens the scholar could gain a thorough understanding of the defects of
58 OC13, 252-253. “Dabimus autem in his, etsi non omnium optimam lentium compositionem, quam
investigare longum esset ac forsan impossibile, at ejusmodi quam nobis experientia utilem esse ostendit.”
59 OC13, 258-265. Discussed above, section 2.1.2..
60 OC13, 262-263. “… res visas, atque etiam distinctiores efficere, nullisque colorum pigmentis infectas
quod in hic lentium trium compositione aegre vitari potest.”
61 OC13, 264-265. “Alij vero aliter lentes oculares in his inter se consociant, sola experientia duce quid
optimum sit quaerentes. nec sane facile foret certa ratione aliquid circa haec praecipere, quum colorum
consideratio ad geometriae leges revocari nequeat, …”
62 A way to reduce colors that was more commonly employed, was to make objective lenses with large
focal distances. These, however, had the drawback that telescopes became very long and tubes too heavy
to remain straight. In 1662, it occurred to Huygens that this could be circumvented by making a tubeless
telescope. He realized it much later and published a little tract on it, Astroscopia Compendiaria (1684). OC21,
201-231.