Lenses and Waves

148 CHAPTER 4
Figure 52 Construction for strangely refracted rays in the principal section
outside the principal section the refracted perpendicular NLS came into view
as an important line of reference. Bartholinus’ analysis had been fully based
on the unrefracted oblique ray. He had not assigned special significance to
the refracted perpendicular. The refracted perpendicular promptly suggested
an alternative law, which Huygens elaborated on the next, third page of his
investigation.
Huygens began with a new drawing of
the principal section (Figure 52). In DBCF are
given the normal to the refracting surface
ABF and the refracted perpendicular ABC,
with FBC slightly smaller than 7. TTC is the
unrefracted oblique ray, parallel to the edge
of the crystal. In the case of ordinary
refraction, Huygens applied the sine law as
he was used to do in his dioptrics. To find
the refraction DD of a ray DF, draw S on BF
so that DS is to DF as the ratio of sines 5 to 3
(or slightly smaller than 8 to 5). Next, he
simply stated the following: in strange
refraction rays DD are refracted towards C,
where the refracted perpendicular reaches the bottom of the crystal. 142 In
other words, strange refraction adds the line FC to the ordinarily refracted
ray. So, to find the strange refraction DC of a ray DD, draw its ordinary
refraction DF and add the line FC. The fact that a parallel component is
added precisely marks the strangeness of strange refraction: the line FC is the
component Iceland crystal ‘strangely’ adds to the perpendicular ray.
142 Hug2, 176r; OC19, 411.
Figure 53 Main lines of Figure 52