Lenses and Waves

1677-1679 –WAVES OF LIGHT 173
depends only on the medium. 41 In other words, Huygens mechanistically
justified his reduction of light propagation to velocity. Consequently, light
consists of waves:
“If light thus takes time for its passage (which we now will examine) it will follow that
this movement impressed on matter is successive; and consequently it spreads, …, by
spherical surfaces and waves: …” 42
After Huygens had shown how light can be
thought to consist of spherical waves propagating
with a considerable yet finite velocity, he moved on
to consider their propagation in more detail. 43 This
is where he finally elaborated his principle of wave
propagation. First of all, each point of a luminous
source produces spherical waves (Figure 64). The
circles represent the propagation of a single wave,
so he added, and should not suggest any regular
succession of particular waves. Although Huygens’
theory is in fact a pulse theory, for sake of
convenience I will speak of waves. While a wave
moves away from its origin, its speed is maintained
although it gradually loses its strength. In the long
run, the waves will become imperceptible to our
Figure 64 Waves around a
source of light
eyes. Still, light produced by such small actions can be perceptible over long
distances, because innumerable waves
“… unite in such a way that to the senses they make up only one single wave, that
consequently must have enough force to make itself felt.” 44
In a ‘Particular remark on the extension of light’, Huygens went on to
describe this uniting more precisely. It was an elaboration of the premise he
had formulated earlier in his discussion of caustics: “The common tangent
curve of all the particular waves will be the propagation of the principal wave
…”. Although he introduced this principle of wave propagation as a
‘remark’, it was the core of Huygens’ theory. Waves of light were not his
idea; his contribution consisted of this principle:
“This is what was not known to those who previously began to consider the waves of
light, among whom are Mr. Hooke in his Micrographia, and father Pardies, who in a
treatise of which he has shown me a part, …, undertook to prove by these waves the
41 The notes on caustics already reveal that the speed of propagation had become central for Huygens.
Implicitly, he constructed the refracted wave by considering rays as isochronous paths. He explicitly
considered the caustic as a path travelled in a specific time, when he showed that its length is equal to a
rectilinear distance traveled by light.
42 Traité, 4. “Que si avec cela la lumiere employe du temps à son passage; ce que nous allons examiner
maintenant; il s’ensuivra que ce mouvement imprimé à la matiere est successif, & que par consequent il
s’etend, … , par des surfaces & des ondes spheriques: …”
43 Traité, 15-17.
44 Traité, 17. “… s’unissent en sorte que sensiblement elles ne composent qu’une onde seule, qui par
consequent doit avoir assez de force pour se faire sentir.”