Lenses and Waves

146 CHAPTER 4
directed to the perpendicular to
the surface.” 135 Bartholinus
reproduced the Cartesian diagram
of the sine law and added the lines
governing strange refraction
(Figure 50). QGS is the face of the
crystal, DN the normal governing
ordinary refraction. FGL is an
ordinarily refracted ray, so FK : LN
is constant. Bartholinus had
determined empirically the index
of (ordinary) refraction for the
crysal FK : LN = 5 : 3. CP is the
unrefracted oblique ray parallel to
the edge of the crystal. It governs
strange refraction in the same way as DN does its ordinary counterpart.
Consequently, when FGM is an extraordinarily refracted ray, the sines FI and
PM are in constant ratio, namely 5 : 3. 136
It is clear that Bartholinus’ law of strange refraction was an extension of
Descartes’ law of ordinary refraction. According to Pedersen and Buchwald,
the leading idea behind Bartholinus’ law of strange refraction was to preserve
Descartes’ sine law of refraction, changing only its frame of reference.
Strange refraction is strange because its ‘normal’ is oblique to the refracting
surface rather than perpendicular. In one sentence, Bartholinus suggested a
physical explanation of the law, which resembled Descartes’ explanation of
ordinary refraction:
“For it appears that this birefringent crystal has pores running along the faces and
parallel to them, since we may observe that the fracture and separation of fragments
follows this disposition of the sides; and [further] one image, namely the mobile one,
passes through these same [pores].” 137
He seems to have adopted Descartes’ theory of light, but he did not
elaborate a causal analysis of strange refraction. Buchwald and Pedersen
point out that Bartholinus expressly distinguished the mathematical law and
the physical structure regarding strange refraction. 138 Figure 50 Bartholinus’ law of strange refraction.
His sole objective was to
establish the law governing the behavior of strangely refracted rays. In his
view he had succeeded in formulating a law from which its observed
properties could be derived. He had also suggested an experiment further to
substantiate it. In the fourteenth experiment, he discussed refraction in
planes that are not parallel to the natural faces of the crystal. He claimed that
135
Bartholinus, Experimenta, 32. Translation by Archibald.
136
Bartholinus, Experimenta, 46-48. Modern notation: sin(i – 17):sin(r – 17) = 5:3; Lohne, “Nova
experimenta”, 142.
137
Bartholinus, Experimenta, 54. Translation by Archibald.
138
Bartholinus, Experiments, 18-19 (Introduction).