Lenses and Waves

THE 'PROJET' OF 1672 147
the fixed and the mobile image would swap place, but had not been able to
substantiate this, as he could not cut the crystal appropriately. 139
Huygens’ alternatives
Huygens followed Bartholinus’ approach to consider only the observed
properties of strangely refracted rays. He adopted the Dane’s data and he
even seems to follow him in his line of thinking: to extend Descartes’
account of ordinary refraction. Nevertheless, Huygens’ analysis differs in two
respects. In the first place he changed perspective by focusing on the
refracted perpendicular ray instead of the unrefracted oblique ray. Which is
not unexpected, for the refraction of the perpendicular ray formed the heart
of the ‘difficulté’ of strange refraction. Accordingly, the one original datum
Huygens supplied was the angle of the refracted perpendicular: slightly
smaller than 7 o. 140 Secondly, he went beyond Bartholinus by considering rays
outside the principal section. The outcome was a new law of strange
refraction.
Having described the crystal,
Huygens began his analysis by
drawing the principal section and
some rays (Figure 51). This plane is
formed by the edge of the crystal
and the line AB that bisects the
obtuse angle of the upper face of
the crystal. The perpendicular ray
GH is refracted to HE. This meant,
according to Huygens, that each ray
in plane GH – the plane through
GH, perpendicular to the paper – is
refracted into the plane HE. KLE is
the unrefracted oblique ray (parallel
to the edge of the crystal through
B). Now, Huygens writes, the
Figure 51 Rays in the principal section.
refraction of rays in plane KL (the plane through KL, perpendicular to the
paper) that are not parallel to ray KL, do not lie in plane LE. These rays
outside the principal section are refracted towards the perpendicular, and the
more oblique they are to KL, the closer their refractions are to the plane
through LS, the refracted perpendicular. 141
By considering rays outside the principal section, Huygens surpassed
Bartholinus’ account. The ‘oblique’ sine law applied only to rays in the
principal section and therefore was not a general law. By considering rays
139
Bartholinus, Experimenta, 22-24.
140
Hug2, 175v; OC19, 410 “Angulus FBC refractionis radii perpendicularis est paulo minor 7 grad. cum ad
solis radios inquiritur.” The reference is to Figure 51.
141
Hug2, 175v; OC19, 410 “… introrsum versus perpendicularem refringuntur ut in LS, idque tanto magis
quanto erunt ad KL radium obliquiores.”