Lenses and Waves

THE 'PROJET' OF 1672 145
Figure 49 Refraction in two positions of the crystal.
The mobile image contradicts the ordinary laws of refraction, but it does
not “seem to vary with uncertain laws”, so Bartholinus began his fifteenth
experiment. 134 To deduce the ‘laws’ governing strange refraction, he recorded
some empirical properties. The mobile image rotates around the fixed image
and does not describe a perfect circle. When the eye is in O, the separations
DC and CB of the images for two positions of the crystal are unequal. When
the eye is in N, on the other hand, the separations QC and CP are the same.
The properties Bartholinus employed to define strange refraction consisted
of qualitative observations where the behavior of strangely refracted rays is
linked to the crystallographic data. This also applies to the observation
crucial to his law of strange refraction: a ray parallel to the edge of the crystal
is not refracted. This probably was a naked eye observation and, as we will
see in the next chapter, it was inaccurate. He did not perform direct optical
measurements of strange refraction. From these rather meager data,
Bartholinus concluded that the mobile image does describe a perfect circle
when the eye is in N.
After seventeen experiments, Bartholinus was ready to formulate a law of
strange refraction: a mathematical construction explaining how to construct
the strange refraction of a ray in the principal section. Bartholinus’ solution is
ingenious; we may surmise his line of thought like the following. As the sine
law does not apply to strange refraction, refractions cannot be measured with
reference to the normal of the refracting plane. Some other instance of
reference should be found, and this was the oblique ray that passed the
surface unrefracted: “… the extraordinary refraction took for its normal a
parallel to the sides of the birefringent crystal, while the ordinary refraction is
134 Bartholinus, Experimenta, 24. Translation by Archibald.