Lenses and Waves

1677-1679 –WAVES OF LIGHT 169
some more sketches and numbers calculations. Then a glorious EUPHKA
follows:
“EUPHKA. 6 August 1677. The cause of strange refraction in Iceland crystal.” 35
The page contains a large drawing of this ‘cause’, surrounded by explanatory
texts and additional drawings and calculations. In the central figure the
oblique ellipse returns, now abundantly rigged up with geometry. The editors
of the Oeuvres Complètes have proposed a plausible order in which the texts
around it have been written. This means that Huygens started with the figure
reproduced in Figure 62, then wrote the ‘Eureka’ at the top-right corner and
started the explanation of the drawing, continuing in the top-left corner with
a smaller sketch and further notes.
Figure 62 “Causam mirae refractionis in Crystallo Islandica”.
The explanation begins with a description of the figure. The crystal has a
principal section for each dimension and AS, the axis of the obtuse solid
angle of the crystal, is the intersection of these (from the center diagonally
down to the right). The plane of the paper is one of the principal sections.
The upper face of the crystal is KA, the lower face D, and AC (from the
center down second to the left) is parallel to the edge of the crystal. AC is
also the unrefracted oblique ray (i.e. parallel to the edge of the crystal). Also
drawn is AB, the refracted perpendicular (from the center down first to the
left). BPSHN is an ellipse, with a circle drawn inside it with center A and
radius AS. The ellipse and circle therefore touch in S. The axis of the ellipse
AP (from the center diagonally down to the left) is normal to AS.
Huygens showed that D is tangent to the ellipse in point B, its
intersection with the refracted perpendicular AB. The smaller ellipse is
constructed by drawing the quadrangle µLA (µ parallel to the tangent of
35 Hug9, 47r. OC19, 427, it is preceded by a facsimile of this manuscript page. “EUPHKA. 6 Aug 1677.
Causam miræ refractionis in Crystallo Islandica.”