Treatise on Light by Christiaan Huygens
C >>
Christiaan Huygens >> Treatise on Light
Pages:
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 Note: Project Gutenberg also has an HTML version of this
file which includes the original illustrations.
See 14725-h.htm or 14725-h.zip:
(http://www.gutenberg.net/dirs/1/4/7/2/14725/14725-h/14725-h.htm)
or
(http://www.gutenberg.net/dirs/1/4/7/2/14725/14725-h.zip)
TREATISE ON LIGHT
In which are explained
The causes of that which occurs
In REFLEXION, & in REFRACTION
And particularly
In the strange REFRACTION
OF ICELAND CRYSTAL
by
CHRISTIAAN HUYGENS
Rendered into English by
SILVANUS P. THOMPSON
University of Chicago Press
PREFACE
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, Roemer, 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.
CHAPTER I
ON RAYS PROPAGATED IN STRAIGHT LINES
As happens in all the sciences in which Geometry is applied to matter,
the demonstrations concerning Optics are founded on truths drawn from
experience. Such are that the rays of light are propagated in straight
lines; that the angles of reflexion and of incidence are equal; and
that in refraction the ray is bent according to the law of sines, now
so well known, and which is no less certain than the preceding laws.
The majority of those who have written touching the various parts of
Optics have contented themselves with presuming these truths. But
some, more inquiring, have desired to investigate the origin and the
causes, considering these to be in themselves wonderful effects of
Nature. In which they advanced some ingenious things, but not however
such that the most intelligent folk do not wish for better and more
satisfactory explanations. Wherefore I here desire to propound what I
have meditated on the subject, so as to contribute as much as I can
to the explanation of this department of Natural Science, which, not
without reason, is reputed to be one of its most difficult parts. I
recognize myself to be much indebted to those who were the first to
begin to dissipate the strange obscurity in which these things were
enveloped, and to give us hope that they might be explained by
intelligible reasoning. But, on the other hand I am astonished also
that even here these have often been willing to offer, as assured and
demonstrative, reasonings which were far from conclusive. For I do not
find that any one has yet given a probable explanation of the first
and most notable phenomena of light, namely why it is not propagated
except in straight lines, and how visible rays, coming from an
infinitude of diverse places, cross one another without hindering one
another in any way.
I shall therefore essay in this book, to give, in accordance with the
principles accepted in the Philosophy of the present day, some clearer
and more probable reasons, firstly of these properties of light
propagated rectilinearly; secondly of light which is reflected on
meeting other bodies. Then I shall explain the phenomena of those rays
which are said to suffer refraction on passing through transparent
bodies of different sorts; and in this part I shall also explain the
effects of the refraction of the air by the different densities of the
Atmosphere.
Thereafter I shall examine the causes of the strange refraction of a
certain kind of Crystal which is brought from Iceland. And finally I
shall treat of the various shapes of transparent and reflecting bodies
by which rays are collected at a point or are turned aside in various
ways. From this it will be seen with what facility, following our new
Theory, we find not only the Ellipses, Hyperbolas, and other curves
which Mr. Des Cartes has ingeniously invented for this purpose; but
also those which the surface of a glass lens ought to possess when its
other surface is given as spherical or plane, or of any other figure
that may be.
It is inconceivable to doubt that light consists in the motion of some
sort of matter. For whether one considers its production, one sees
that here upon the Earth it is chiefly engendered by fire and flame
which contain without doubt bodies that are in rapid motion, since
they dissolve and melt many other bodies, even the most solid; or
whether one considers its effects, one sees that when light is
collected, as by concave mirrors, it has the property of burning as a
fire does, that is to say it disunites the particles of bodies. This
is assuredly the mark of motion, at least in the true Philosophy, in
which one conceives the causes of all natural effects in terms of
mechanical motions. This, in my opinion, we must necessarily do, or
else renounce all hopes of ever comprehending anything in Physics.
And as, according to this Philosophy, one holds as certain that the
sensation of sight is excited only by the impression of some movement
of a kind of matter which acts on the nerves at the back of our eyes,
there is here yet one reason more for believing that light consists in
a movement of the matter which exists between us and the luminous
body.
Further, when one considers the extreme speed with which light spreads
on every side, and how, when it comes from different regions, even
from those directly opposite, the rays traverse one another without
hindrance, one may well understand that when we see a luminous object,
it cannot be by any transport of matter coming to us from this object,
in the way in which a shot or an arrow traverses the air; for
assuredly that would too greatly impugn these two properties of light,
especially the second of them. It is then in some other way that light
spreads; and that which can lead us to comprehend it is the knowledge
which we have of the spreading of Sound in the air.
We know that by means of the air, which is an invisible and impalpable
body, Sound spreads around the spot where it has been produced, by a
movement which is passed on successively from one part of the air to
another; and that the spreading of this movement, taking place equally
rapidly on all sides, ought to form spherical surfaces ever enlarging
and which strike our ears. Now there is no doubt at all that light
also comes from the luminous body to our eyes by some movement
impressed on the matter which is between the two; since, as we have
already seen, it cannot be by the transport of a body which passes
from one to the other. If, in addition, light takes time for its
passage--which we are now going to examine--it will follow that this
movement, impressed on the intervening matter, is successive; and
consequently it spreads, as Sound does, by spherical surfaces and
waves: for I call them waves from their resemblance to those which are
seen to be formed in water when a stone is thrown into it, and which
present a successive spreading as circles, though these arise from
another cause, and are only in a flat surface.
To see then whether the spreading of light takes time, let us consider
first whether there are any facts of experience which can convince us
to the contrary. As to those which can be made here on the Earth, by
striking lights at great distances, although they prove that light
takes no sensible time to pass over these distances, one may say with
good reason that they are too small, and that the only conclusion to
be drawn from them is that the passage of light is extremely rapid.
Mr. Des Cartes, who was of opinion that it is instantaneous, founded
his views, not without reason, upon a better basis of experience,
drawn from the Eclipses of the Moon; which, nevertheless, as I shall
show, is not at all convincing. I will set it forth, in a way a little
different from his, in order to make the conclusion more
comprehensible.
[Illustration]
Let A be the place of the sun, BD a part of the orbit or annual path
of the Earth: ABC a straight line which I suppose to meet the orbit of
the Moon, which is represented by the circle CD, at C.
Now if light requires time, for example one hour, to traverse the
space which is between the Earth and the Moon, it will follow that the
Earth having arrived at B, the shadow which it casts, or the
interruption of the light, will not yet have arrived at the point C,
but will only arrive there an hour after. It will then be one hour
after, reckoning from the moment when the Earth was at B, that the
Moon, arriving at C, will be obscured: but this obscuration or
interruption of the light will not reach the Earth till after another
hour. Let us suppose that the Earth in these two hours will have
arrived at E. The Earth then, being at E, will see the Eclipsed Moon
at C, which it left an hour before, and at the same time will see the
sun at A. For it being immovable, as I suppose with Copernicus, and
the light moving always in straight lines, it must always appear where
it is. But one has always observed, we are told, that the eclipsed
Moon appears at the point of the Ecliptic opposite to the Sun; and yet
here it would appear in arrear of that point by an amount equal to the
angle GEC, the supplement of AEC. This, however, is contrary to
experience, since the angle GEC would be very sensible, and about 33
degrees. Now according to our computation, which is given in the
Treatise on the causes of the phenomena of Saturn, the distance BA
between the Earth and the Sun is about twelve thousand diameters of
the Earth, and hence four hundred times greater than BC the distance
of the Moon, which is 30 diameters. Then the angle ECB will be nearly
four hundred times greater than BAE, which is five minutes; namely,
the path which the earth travels in two hours along its orbit; and
thus the angle BCE will be nearly 33 degrees; and likewise the angle
CEG, which is greater by five minutes.
But it must be noted that the speed of light in this argument has been
assumed such that it takes a time of one hour to make the passage from
here to the Moon. If one supposes that for this it requires only one
minute of time, then it is manifest that the angle CEG will only be 33
minutes; and if it requires only ten seconds of time, the angle will
be less than six minutes. And then it will not be easy to perceive
anything of it in observations of the Eclipse; nor, consequently, will
it be permissible to deduce from it that the movement of light is
instantaneous.
It is true that we are here supposing a strange velocity that would be
a hundred thousand times greater than that of Sound. For Sound,
according to what I have observed, travels about 180 Toises in the
time of one Second, or in about one beat of the pulse. But this
supposition ought not to seem to be an impossibility; since it is not
a question of the transport of a body with so great a speed, but of a
successive movement which is passed on from some bodies to others. I
have then made no difficulty, in meditating on these things, in
supposing that the emanation of light is accomplished with time,
seeing that in this way all its phenomena can be explained, and that
in following the contrary opinion everything is incomprehensible. For
it has always seemed tome that even Mr. Des Cartes, whose aim has been
to treat all the subjects of Physics intelligibly, and who assuredly
has succeeded in this better than any one before him, has said nothing
that is not full of difficulties, or even inconceivable, in dealing
with Light and its properties.
But that which I employed only as a hypothesis, has recently received
great seemingness as an established truth by the ingenious proof of
Mr. Roemer which I am going here to relate, expecting him himself to
give all that is needed for its confirmation. It is founded as is the
preceding argument upon celestial observations, and proves not only
that Light takes time for its passage, but also demonstrates how much
time it takes, and that its velocity is even at least six times
greater than that which I have just stated.
For this he makes use of the Eclipses suffered by the little planets
which revolve around Jupiter, and which often enter his shadow: and
see what is his reasoning. Let A be the Sun, BCDE the annual orbit of
the Earth, F Jupiter, GN the orbit of the nearest of his Satellites,
for it is this one which is more apt for this investigation than any
of the other three, because of the quickness of its revolution. Let G
be this Satellite entering into the shadow of Jupiter, H the same
Satellite emerging from the shadow.
[Illustration]
Let it be then supposed, the Earth being at B some time before the
last quadrature, that one has seen the said Satellite emerge from the
shadow; it must needs be, if the Earth remains at the same place,
that, after 42-1/2 hours, one would again see a similar emergence,
because that is the time in which it makes the round of its orbit, and
when it would come again into opposition to the Sun. And if the Earth,
for instance, were to remain always at B during 30 revolutions of this
Satellite, one would see it again emerge from the shadow after 30
times 42-1/2 hours. But the Earth having been carried along during
this time to C, increasing thus its distance from Jupiter, it follows
that if Light requires time for its passage the illumination of the
little planet will be perceived later at C than it would have been at
B, and that there must be added to this time of 30 times 42-1/2 hours
that which the Light has required to traverse the space MC, the
difference of the spaces CH, BH. Similarly at the other quadrature
when the earth has come to E from D while approaching toward Jupiter,
the immersions of the Satellite ought to be observed at E earlier than
they would have been seen if the Earth had remained at D.
Pages:
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9