Lenses and Waves

THE 'PROJET' OF 1672 141
Figure 44 Sketch of refracted rays in Iceland crystal: r (‘regelmatig’) for
ordinary refraction; o (‘onregelmatig’) for strange refraction.
On 8 July 1672, Pardies wrote Huygens about strange refraction. He had
visited Picard and taken a look at a piece of Iceland crystal brought from
Denmark. Pardies did not believe the phenomenon contradicted the sine
law, as he thought it could be explained from the composition of the crystal.
“… it seems to me that it is not as troublesome as I had imagined to explain this effect.
… I am very much mistaken if one cannot demonstrate that, if one were to cut various
pieces of glass in rhomboid shape and simply put one on the other to make a total
rhomboid out of them, two refractions would present themselves.” 123
Some sketches Huygens made in his notebook
around the same time are reminiscent of Pardies’
view (Figure 45). They seem to explore how the
composition of the crystal may explain strange
refraction. The surface is drawn indented, so that
part of the perpendicularly incident light actually
falls on an oblique surface. A perpendicular ray
falls upon the indented surface so that part of the
wave is divided into many small wavelets, that
proceed obliquely to the surface. 124
Apparently, Huygens did not accept Pardies’ idea, for he did not
elaborate it beyond these sketches. Moreover, he ended his first study with
the conclusion that the refracted perpendicular contradicted the wave
explanation of refraction. 125 A sketch on the next page of his notebook makes
123 OC7, 193. “… il me semble qu’il n’est pas si malaisé que je m’estois imaginé, d’expliquer cét effet. Je
suis fort trompé si l’on ne peut démonstrer que si l’on taillait plusiers pieces de verre en rhomboide et
qu’on les mit simplement l’une sur l’autre pour en faire un rhomboide total, il s’y feroit deux refractions.”
124 Hug2, 178v; OC19, 415.
125 See below page 151 footnote 148.
Figure 45 A refracted
perpendicular caused by the
composition of the crystal.