Lenses and Waves

1677-1679 –WAVES OF LIGHT 197
refrangibility was an observational property derived from experiment. In his
paper on colors of 1672 he remained silent on the mechanistic nature of light
and colors, and in his lectures on optics he likewise kept his mouth shut. In a
paper Newton sent Oldenburg a few years later, on 7 December 1675, he
disclosed his views in public for the first time. “An Hypothesis explaining
the Properties of Light discoursed of in my severall Papers” it was called. It
gave qualitative explanations for reflection, refraction and the diversity of
colors.
Twelve years later, in Principia, Newton mathematized the explanation of
the sine law sketched in the ‘Hypothesis’. However, he did not present it
explicitly as a derivation of the sine law. Section XIV of Book I discussed
“The motion of minimally small bodies that are acted on by centripetal
forces tending towards each of the individual parts of some great body”. 114
Only in a scholium after the exposition did Newton point out the
resemblance of the results here obtained with the behavior of light rays. He
added cautiously:
“Therefor because of the analogy that exists between the propagation of rays of light
and the motion of bodies, I have decided to subjoin the following propositions for
optical uses, meanwhile not arguing at all about the nature of rays (that is, whether they
are bodies or not), but only determining the trajectories of bodies, which are very
similar to the trajectories of rays.” 115
In proposition 94, Newton pictured (Figure 74) a space AabB between two
similar media, bounded by parallel planes, through which a body passes that
is attracted or impelled perpendicularly towards either of those media and
showed “… that the sine of the angle of incidence onto either plane will be
to the sine of the angle of emergence from the other plane in a given
ratio.” 116
A body moves along GH
and is attracted upwards
between Aa and Bb. During
its passage it follows the
curve HI, then leaves the
layer along IK. The curve is
constructed by producing
GH to M and IK to L,
drawing IM perpendicular to
Bb, and a semi-circle PNIQ
with center L and radius LI.
Newton then showed that
when the attraction is
uniform, HI will be part of a
parabola with the following
Figure 74 Refraction in Principia.
114 Newton, Principia, 622.
115 Newton, Principia, 622- 626. The following propositions were on anaclastics.
116 Newton, Principia, 622.