TREATISE ON LIGHT
Christiaan Huygens
PREFACE
In which are explained
the causes of that which occurs
In REFLEXION, & in REFRACTION
and particularly
in the strange REFRACTION
OF ICELAND CRYSTAL
Preface | Chapter 1 | Chaper 2 | Chapter 3 | Chapter 4 | Chapter 5 | Chapter 6
I wrote this Treatise during my sojourn in France twelve years ago,
and I communicated it in the year 1678 to the learned persons who then
composed the Royal Academy of Science, to the membership of which the
King had done me the honour of calling, me. Several of that body who
are still alive will remember having been present when I read it, and
above the rest those amongst them who applied themselves particularly
to the study of Mathematics; of whom I cannot cite more than the
celebrated gentlemen Cassini, Römer, and De la Hire. And, although I
have since corrected and changed some parts, the copies which I had
made of it at that time may serve for proof that I have yet added
nothing to it save some conjectures touching the formation of Iceland
Crystal, and a novel observation on the refraction of Rock Crystal. I
have desired to relate these particulars to make known how long I have
meditated the things which now I publish, and not for the purpose of
detracting from the merit of those who, without having seen anything
that I have written, may be found to have treated of like matters: as
has in fact occurred to two eminent Geometricians, Messieurs Newton
and Leibnitz, with respect to the Problem of the figure of glasses for
collecting rays when one of the surfaces is given.
One may ask why I have so long delayed to bring this work to the
light. The reason is that I wrote it rather carelessly in the Language
in which it appears, with the intention of translating it into Latin,
so doing in order to obtain greater attention to the thing. After
which I proposed to myself to give it out along with another Treatise
on Dioptrics, in which I explain the effects of Telescopes and those
things which belong more to that Science. But the pleasure of novelty
being past, I have put off from time to time the execution of this
design, and I know not when I shall ever come to an end if it, being
often turned aside either by business or by some new study.
Considering which I have finally judged that it was better worth while
to publish this writing, such as it is, than to let it run the risk,
by waiting longer, of remaining lost.
There will be seen in it demonstrations of those kinds which do not
produce as great a certitude as those of Geometry, and which even
differ much therefrom, since whereas the Geometers prove their
Propositions by fixed and incontestable Principles, here the
Principles are verified by the conclusions to be drawn from them; the
nature of these things not allowing of this being done otherwise.
It is always possible to attain thereby to a degree of probability
which very often is scarcely less than complete proof. To wit, when
things which have been demonstrated by the Principles that have been
assumed correspond perfectly to the phenomena which experiment has
brought under observation; especially when there are a great number of
them, and further, principally, when one can imagine and foresee new
phenomena which ought to follow from the hypotheses which one employs,
and when one finds that therein the fact corresponds to our prevision.
But if all these proofs of probability are met with in that which I
propose to discuss, as it seems to me they are, this ought to be a
very strong confirmation of the success of my inquiry; and it must be
ill if the facts are not pretty much as I represent them. I would
believe then that those who love to know the Causes of things and who
are able to admire the marvels of Light, will find some satisfaction
in these various speculations regarding it, and in the new explanation
of its famous property which is the main foundation of the
construction of our eyes and of those great inventions which extend so
vastly the use of them.
I hope also that there will be some who by following these beginnings
will penetrate much further into this question than I have been able
to do, since the subject must be far from being exhausted. This
appears from the passages which I have indicated where I leave certain
difficulties without having resolved them, and still more from matters
which I have not touched at all, such as Luminous Bodies of several
sorts, and all that concerns Colours; in which no one until now can
boast of having succeeded. Finally, there remains much more to be
investigated touching the nature of Light which I do not pretend to
have disclosed, and I shall owe much in return to him who shall be
able to supplement that which is here lacking to me in knowledge. The
Hague. The 8 January 1690.
NOTE BY THE TRANSLATOR
Considering the great influence which this Treatise has exercised in
the development of the Science of Optics, it seems strange that two
centuries should have passed before an English edition of the work
appeared. Perhaps the circumstance is due to the mistaken zeal with
which formerly everything that conflicted with the cherished ideas of
Newton was denounced by his followers. The Treatise on Light of
Huygens has, however, withstood the test of time: and even now the
exquisite skill with which he applied his conception of the
propagation of waves of light to unravel the intricacies of the
phenomena of the double refraction of crystals, and of the refraction
of the atmosphere, will excite the admiration of the student of
Optics. It is true that his wave theory was far from the complete
doctrine as subsequently developed by Thomas Young and Augustin
Fresnel, and belonged rather to geometrical than to physical Optics.
If Huygens had no conception of transverse vibrations, of the
principle of interference, or of the existence of the ordered sequence
of waves in trains, he nevertheless attained to a remarkably clear
understanding of the principles of wave-propagation; and his
exposition of the subject marks an epoch in the treatment of Optical
problems. It has been needful in preparing this translation to
exercise care lest one should import into the author's text ideas of
subsequent date, by using words that have come to imply modern
conceptions. Hence the adoption of as literal a rendering as possible.
A few of the author's terms need explanation. He uses the word
"refraction," for example, both for the phenomenon or process usually
so denoted, and for the result of that process: thus the refracted ray
he habitually terms "the refraction" of the incident ray. When a
wave-front, or, as he terms it, a "wave," has passed from some initial
position to a subsequent one, he terms the wave-front in its
subsequent position "the continuation" of the wave. He also speaks of
the envelope of a set of elementary waves, formed by coalescence of
those elementary wave-fronts, as "the termination" of the wave; and
the elementary wave-fronts he terms "particular" waves. Owing to the
circumstance that the French word _rayon_ possesses the double
signification of ray of light and radius of a circle, he avoids its
use in the latter sense and speaks always of the semi-diameter, not of
the radius. His speculations as to the ether, his suggestive views of
the structure of crystalline bodies, and his explanation of opacity,
slight as they are, will possibly surprise the reader by their seeming
modernness. And none can read his investigation of the phenomena found
in Iceland spar without marvelling at his insight and sagacity.
S.P.T.
June, 1912.
TABLE OF MATTERS
Contained in this Treatise
CHAPTER I.
On Rays Propagated in Straight Lines.
That Light is produced by a certain movement.
That no substance passes from the luminous object to the eyes.
That Light spreads spherically, almost as Sound does.
Whether Light takes time to spread.
Experience seeming to prove that it passes instantaneously.
Experience proving that it takes time.
How much its speed is greater than that of Sound.
In what the emission of Light differs from that of Sound.
That it is not the same medium which serves for Light and Sound.
How Sound is propagated.
How Light is propagated.
Detailed Remarks on the propagation of Light.
Why Rays are propagated only in straight lines.
How Light coming in different directions can cross itself.
CHAPTER II.
On Reflexion.
Demonstration of equality of angles of incidence and reflexion.
Why the incident and reflected rays are in the same plane
perpendicular to the reflecting surface.
That it is not needful for the reflecting surface to be perfectly
flat to attain equality of the angles of incidence and reflexion.
CHAPTER III.
On Refraction.
That bodies may be transparent without any substance passing through
them.
Proof that the ethereal matter passes through transparent bodies.
How this matter passing through can render them transparent.
That the most solid bodies in appearance are of a very loose texture.
That Light spreads more slowly in water and in glass than in air.
Third hypothesis to explain transparency, and the retardation which
Light suffers.
On that which makes bodies opaque.
Demonstration why Refraction obeys the known proportion of Sines.
Why the incident and refracted Rays produce one another reciprocally.
Why Reflexion within a triangular glass prism is suddenly augmented
when the Light can no longer penetrate.
That bodies which cause greater Refraction also cause stronger
Reflexion.
Demonstration of the Theorem of Mr. Fermat.
CHAPTER IV.
On the Refraction of the Air.
That the emanations of Light in the air are not spherical.
How consequently some objects appear higher than they are.
How the Sun may appear on the Horizon before he has risen.
That the rays of light become curved in the Air of the Atmosphere,
and what effects this produces.
CHAPTER V.
On the Strange Refraction of Iceland Crystal.
That this Crystal grows also in other countries.
Who first-wrote about it.
Description of Iceland Crystal; its substance, shape, and properties.
That it has two different Refractions.
That the ray perpendicular to the surface suffers refraction, and
that some rays inclined to the surface pass without suffering
refraction.
Observation of the refractions in this Crystal.
That there is a Regular and an Irregular Refraction.
The way of measuring the two Refractions of Iceland Crystal.
Remarkable properties of the Irregular Refraction.
Hypothesis to explain the double Refraction.
That Rock Crystal has also a double Refraction.
Hypothesis of emanations of Light, within Iceland Crystal, of
spheroidal form, for the Irregular Refraction.
How a perpendicular ray can suffer Refraction.
How the position and form of the spheroidal emanations in this
Crystal can be defined.
Explanation of the Irregular Refraction by these spheroidal
emanations.
Easy way to find the Irregular Refraction of each incident ray.
Demonstration of the oblique ray which traverses the Crystal without
being refracted.
Other irregularities of Refraction explained.
That an object placed beneath the Crystal appears double, in two
images of different heights.
Why the apparent heights of one of the images change on changing the
position of the eyes above the Crystal.
Of the different sections of this Crystal which produce yet other
refractions, and confirm all this Theory.
Particular way of polishing the surfaces after it has been cut.
Surprising phenomenon touching the rays which pass through two
separated pieces; the cause of which is not explained.
Probable conjecture on the internal composition of Iceland Crystal,
and of what figure its particles are.
Tests to confirm this conjecture.
Calculations which have been supposed in this Chapter.
CHAPTER VI.
On the Figures of transparent bodies which serve for Refraction and
for Reflexion.
General and easy rule to find these Figures.
Invention of the Ovals of Mr. Des Cartes for Dioptrics.
How he was able to find these Lines.
Way of finding the surface of a glass for perfect refraction, when
the other surface is given.
Remark on what happens to rays refracted at a spherical surface.
Remark on the curved line which is formed by reflexion in a spherical
concave mirror.
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