SIX LECTURES ON LIGHT
DELIVERED IN THE UNITED STATES
IN
1872-1873
BY
JOHN TYNDALL, D.C.L., LL,D., F.R.S.
LATE PROFESSOR OF NATURAL PHILOSOPHY IN THE
ROYAL INSTITUTION OF GREAT BRITAIN
[Illustration: Sir Thomas Laurence PRA Pinx
Henry Adlarc. Sc.
Signature: Thomas Young]
London: Longmans & Co.
_SIXTH IMPRESSION_
LONGMANS, GREEN, AND CO.
39 PATERNOSTER ROW, LONDON
NEW YORK AND BOMBAY
1906
PREFACE TO THE FOURTH EDITION.
In these Lectures I have sought to render clear a difficult but
profoundly interesting subject. My aim has been not only to describe
and illustrate in a familiar manner the principal laws and phenomena
of light, but to point out the origin, and show the application, of
the theoretic conceptions which underlie and unite the whole, and
without which no real interpretation is possible.
The Lectures, as stated on the title-page, were delivered in the
United States in 1872-3. I still retain a vivid and grateful
remembrance of the cordiality with which they were received.
My scope and object are briefly indicated in the 'Summary and
Conclusion,' which, as recommended in a former edition, might be, not
unfitly, read as an introduction to the volume.
J.T.
ALP LUSGEN: _October_ 1885.
CONTENTS.
LECTURE I.
Introductory
Uses of Experiment
Early Scientific Notions
Sciences of Observation
Knowledge of the Ancients regarding Light
Defects of the Eye
Our Instruments
Rectilineal Propagation of Light
Law of Incidence and Reflection
Sterility of the Middle Ages
Refraction
Discovery of Snell
Partial and Total Reflection
Velocity of Light
Roemer, Bradley, Foucault, and Fizeau
Principle of Least Action
Descartes and the Rainbow
Newton's Experiments on the Composition of Solar Light
His Mistake regarding Achromatism
Synthesis of White Light
Yellow and Blue Lights produce White by their Mixture
Colours of Natural Bodies
Absorption
Mixture of Pigments contrasted with Mixture of Lights
LECTURE II.
Origin of Physical Theories
Scope of the Imagination
Newton and the Emission Theory
Verification of Physical Theories
The Luminiferous Ether
Wave-theory of Light
Thomas Young
Fresnel and Arago
Conception of Wave-motion
Interference of Waves
Constitution of Sound-waves
Analogies of Sound and Light
Illustrations of Wave-motion
Interference of Sound Waves
Optical Illustrations
Pitch and Colour
Lengths of the Waves of Light and Rates of Vibration of the
Ether-particles
Interference of Light
Phenomena which first suggested the Undulatory Theory
Boyle and Hooke
The Colours of thin Plates
The Soap-bubble
Newton's Rings
Theory of 'Fits'
Its Explanation of the Rings
Overthrow of the Theory
Diffraction of Light
Colours produced by Diffraction
Colours of Mother-of-Pearl.
LECTURE III.
Relation of Theories to Experience
Origin of the Notion of the Attraction of Gravitation
Notion of Polarity, how generated
Atomic Polarity
Structural Arrangements due to Polarity
Architecture of Crystals considered as an Introduction to their
Action upon Light
Notion of Atomic Polarity applied to Crystalline Structure
Experimental Illustrations
Crystallization of Water
Expansion by Heat and by Cold
Deportment of Water considered and explained
Bearings of Crystallization on Optical Phenomena
Refraction
Double Refraction
Polarization
Action of Tourmaline
Character of the Beams emergent from Iceland Spar
Polarization by ordinary Refraction and Reflection
Depolarization.
LECTURE IV.
Chromatic Phenomena produced by Crystals in Polarized Light
The Nicol Prism
Polarizer and Analyzer
Action of Thick and Thin Plates of Selenite
Colours dependent on Thickness
Resolution of Polarized Beam into two others by the Selenite
One of them more retarded than the other
Recompounding of the two Systems of Waves by the Analyzer
Interference thus rendered possible
Consequent Production of Colours
Action of Bodies mechanically strained or pressed
Action of Sonorous Vibrations
Action of Glass strained or pressed by Heat
Circular Polarization
Chromatic Phenomena produced by Quartz
The Magnetization of Light
Rings surrounding the Axes of Crystals
Biaxal and Uniaxal Crystals
Grasp of the Undulatory Theory
The Colour and Polarization of Sky-light
Generation of Artificial Skies.
LECTURE V.
Range of Vision not commensurate with Range of Radiation
The Ultra-violet Rays
Fluorescence
The rendering of invisible Rays visible
Vision not the only Sense appealed to by the Solar and Electric Beam
Heat of Beam
Combustion by Total Beam at the Foci of Mirrors and Lenses
Combustion through Ice-lens
Ignition of Diamond
Search for the Rays here effective
Sir William Herschel's Discovery of dark Solar Rays
Invisible Rays the Basis of the Visible
Detachment by a Ray-filter of the Invisible Rays from the Visible
Combustion at Dark Foci
Conversion of Heat-rays into Light-rays
Calorescence
Part played in Nature by Dark Rays
Identity of Light and Radiant Heat
Invisible Images
Reflection, Refraction, Plane Polarization, Depolarization,
Circular Polarization, Double Refraction, and Magnetization of
Radiant Heat
LECTURE VI.
Principles of Spectrum Analysis
Prismatic Analysis of the Light of Incandescent Vapours
Discontinuous Spectra
Spectrum Bands proved by Bunsen and Kirchhoff to be characteristic
of the Vapour
Discovery of Rubidium, Cæsium, and Thallium
Relation of Emission to Absorption
The Lines of Fraunhofer
Their Explanation by Kirchhoff
Solar Chemistry involved in this Explanation
Foucault's Experiment
Principles of Absorption
Analogy of Sound and Light
Experimental Demonstration of this Analogy
Recent Applications of the Spectroscope
Summary and Conclusion
APPENDIX.
On the Spectra of Polarized Light
Measurement of the Waves of Light
INDEX
ON LIGHT
LECTURE I.
INTRODUCTORY
USES OF EXPERIMENT
EARLY SCIENTIFIC NOTIONS
SCIENCES OF OBSERVATION
KNOWLEDGE OF THE ANCIENTS REGARDING LIGHT
DEFECTS OF THE EYE
OUR INSTRUMENTS
RECTILINEAL PROPAGATION OF LIGHT
LAW OF INCIDENCE AND REFLECTION
STERILITY OF THE MIDDLE AGES
REFRACTION
DISCOVERY OF SNELL
PARTIAL AND TOTAL REFLECTION
VELOCITY OF LIGHT
ROEMER, BRADLEY, FOUCAULT, AND FIZEAU
PRINCIPLE OF LEAST ACTION
DESCARTES AND THE RAINBOW
NEWTON'S EXPERIMENTS ON THE COMPOSITION OF SOLAR LIGHT
HIS MISTAKE AS REGARDS ACHROMATISM
SYNTHESIS OF WHITE LIGHT
YELLOW AND BLUE LIGHTS PRODUCE WHITE BY THEIR MIXTURE
COLOURS OF NATURAL BODIES
ABSORPTION
MIXTURE OF PIGMENTS CONTRASTED WITH MIXTURE OF LIGHTS.
§ 1. _Introduction_.
Some twelve years ago I published, in England, a little book entitled
the 'Glaciers of the Alps,' and, a couple of years subsequently, a
second book, entitled 'Heat a Mode of Motion.' These volumes were
followed by others, written with equal plainness, and with a similar
aim, that aim being to develop and deepen sympathy between science and
the world outside of science. I agreed with thoughtful men[1] who
deemed it good for neither world to be isolated from the other, or
unsympathetic towards the other, and, to lessen this isolation, at
least in one department of science, I swerved, for a time, from those
original researches which have been the real pursuit and pleasure of
my life.
The works here referred to were, for the most part, republished by the
Messrs. Appleton of New York,[2] under the auspices of a man who is
untiring in his efforts to diffuse sound scientific knowledge among
the people of the United States; whose energy, ability, and
single-mindedness, in the prosecution of an arduous task, have won for
him the sympathy and support of many of us in 'the old country.' I
allude to Professor Youmans. Quite as rapidly as in England, the aim
of these works was understood and appreciated in the United States,
and they brought me from this side of the Atlantic innumerable
evidences of good-will. Year after year invitations reached me[3] to
visit America, and last year (1871) I was honoured with a request so
cordial, signed by five-and-twenty names, so distinguished in science,
in literature, and in administrative position, that I at once resolved
to respond to it by braving not only the disquieting oscillations of
the Atlantic, but the far more disquieting ordeal of appearing in
person before the people of the United States.
This invitation, conveyed to me by my accomplished friend Professor
Lesley, of Philadelphia, and preceded by a letter of the same purport
from your scientific Nestor, the celebrated Joseph Henry, of
Washington, desired that I should lecture in some of the principal
cities of the Union. This I agreed to do, though much in the dark as
to a suitable subject. In answer to my inquiries, however, I was given
to understand that a course of lectures, showing the uses of
experiment in the cultivation of Natural Knowledge, would materially
promote scientific education in this country. And though such lectures
involved the selection of weighty and delicate instruments, and their
transfer from place to place, I determined to meet the wishes of my
friends, as far as the time and means at my disposal would allow.
§ 2. _Subject of the Course. Source of Light employed._
Experiments have two great uses--a use in discovery, and a use in
tuition. They were long ago defined as the investigator's language
addressed to Nature, to which she sends intelligible replies. These
replies, however, usually reach the questioner in whispers too feeble
for the public ear. But after the investigator comes the teacher,
whose function it is so to exalt and modify the experiments of his
predecessor, as to render them fit for public presentation. This
secondary function I shall endeavour, in the present instance, to
fulfil.
Taking a single department of natural philosophy as my subject, I
propose, by means of it, to illustrate the growth of scientific
knowledge under the guidance of experiment. I wish, in the first
place, to make you acquainted with certain elementary phenomena; then
to point out to you how the theoretical principles by which phenomena
are explained take root in the human mind, and finally to apply these
principles to the whole body of knowledge covered by the lectures. The
science of optics lends itself particularly well to this mode of
treatment, and on it, therefore, I propose to draw for the materials
of the present course. It will be best to begin with the few simple
facts regarding light which were known to the ancients, and to pass
from them, in historic gradation, to the more abstruse discoveries of
modern times.
All our notions of Nature, however exalted or however grotesque, have
their foundation in experience. The notion of personal volition in
Nature had this basis. In the fury and the serenity of natural
phenomena the savage saw the transcript of his own varying moods, and
he accordingly ascribed these phenomena to beings of like passions
with himself, but vastly transcending him in power. Thus the notion of
_causality_--the assumption that natural things did not come of
themselves, but had unseen antecedents--lay at the root of even the
savage's interpretation of Nature. Out of this bias of the human mind
to seek for the causes of phenomena all science has sprung.
We will not now go back to man's first intellectual gropings; much
less shall we enter upon the thorny discussion as to how the groping
man arose. We will take him at that stage of his development, when he
became possessed of the apparatus of thought and the power of using
it. For a time--and that historically a long one--he was limited to
mere observation, accepting what Nature offered, and confining
intellectual action to it alone. The apparent motions of sun and stars
first drew towards them the questionings of the intellect, and
accordingly astronomy was the first science developed. Slowly, and
with difficulty, the notion of natural forces took root in the human
mind. Slowly, and with difficulty, the science of mechanics had to
grow out of this notion; and slowly at last came the full application
of mechanical principles to the motions of the heavenly bodies. We
trace the progress of astronomy through Hipparchus and Ptolemy; and,
after a long halt, through Copernicus, Galileo, Tycho Brahe, and
Kepler; while from the high table-land of thought occupied by these
men, Newton shoots upwards like a peak, overlooking all others from
his dominant elevation.
But other objects than the motions of the stars attracted the
attention of the ancient world. Light was a familiar phenomenon, and
from the earliest times we find men's minds busy with the attempt to
render some account of it. But without _experiment_, which belongs to
a later stage of scientific development, little progress could be here
made. The ancients, accordingly, were far less successful in dealing
with light than in dealing with solar and stellar motions. Still they
did make some progress. They satisfied themselves that light moved in
straight lines; they knew also that light was reflected from polished
surfaces, and that the angle of incidence was equal to the angle of
reflection. These two results of ancient scientific curiosity
constitute the starting-point of our present course of lectures.
But in the first place it will be useful to say a few words regarding
the source of light to be employed in our experiments. The rusting of
iron is, to all intents and purposes, the slow burning of iron. It
develops heat, and, if the heat be preserved, a high temperature may
be thus attained. The destruction of the first Atlantic cable was
probably due to heat developed in this way. Other metals are still
more combustible than iron. You may ignite strips of zinc in a candle
flame, and cause them to burn almost like strips of paper. But we must
now expand our definition of combustion, and include under this term,
not only combustion in air, but also combustion in liquids. Water, for
example, contains a store of oxygen, which may unite with, and
consume, a metal immersed in it; it is from this kind of combustion
that we are to derive the heat and light employed in our present
course.
The generation of this light and of this heat merits a moment's
attention. Before you is an instrument--a small voltaic battery--in
which zinc is immersed in a suitable liquid. An attractive force is at
this moment exerted between the metal and the oxygen of the liquid;
actual combination, however, being in the first instance avoided.
Uniting the two ends of the battery by a thick wire, the attraction is
satisfied, the oxygen unites with the metal, zinc is consumed, and
heat, as usual, is the result of the combustion. A power which, for
want of a better name, we call an electric current, passes at the same
time through the wire.
Cutting the thick wire in two, let the severed ends be united by a
thin one. It glows with a white heat. Whence comes that heat? The
question is well worthy of an answer. Suppose in the first instance,
when the thick wire is employed, that we permit the action to continue
until 100 grains of zinc are consumed, the amount of heat generated in
the battery would be capable of accurate numerical expression. Let
the action then continue, with the thin wire glowing, until 100 grains
of zinc are consumed. Will the amount of heat generated in the battery
be the same as before? No; it will be less by the precise amount
generated in the thin wire outside the battery. In fact, by adding the
internal heat to the external, we obtain for the combustion of 100
grains of zinc a total which never varies. We have here a beautiful
example of that law of constancy as regards natural energies, the
establishment of which is the greatest achievement of modern science.
By this arrangement, then, we are able to burn our zinc at one place,
and to exhibit the effects of its combustion at another. In New York,
for example, we may have our grate and fuel; but the heat and light of
our fire may be made to appear at San Francisco.
[Illustration: Fig. 1.]
Removing the thin wire and attaching to the severed ends of the thick
one two rods of coke we obtain, on bringing the rods together (as in
fig. 1), a small star of light. Now, the light to be employed in our
lectures is a simple exaggeration of this star. Instead of being
produced by ten cells, it is produced by fifty. Placed in a suitable
camera, provided with a suitable lens, this powerful source will give
us all the light necessary for our experiments.
And here, in passing, I am reminded of the common delusion that the
works of Nature, the human eye included, are theoretically perfect.
The eye has grown for ages _towards_ perfection; but ages of
perfecting may be still before it. Looking at the dazzling light from
our large battery, I see a luminous globe, but entirely fail to see
the shape of the coke-points whence the light issues. The cause may be
thus made clear: On the screen before you is projected an image of the
carbon points, the _whole_ of the glass lens in front of the camera
being employed to form the image. It is not sharp, but surrounded by a
halo which nearly obliterates the carbons. This arises from an
imperfection of the glass lens, called its _spherical aberration_,
which is due to the fact that the circumferential and central rays
have not the same focus. The human eye labours under a similar defect,
and from this, and other causes, it arises that when the naked light
from fifty cells is looked at the blur of light upon the retina is
sufficient to destroy the definition of the retinal image of the
carbons. A long list of indictments might indeed be brought against
the eye--its opacity, its want of symmetry, its lack of achromatism,
its partial blindness. All these taken together caused Helmholt to say
that, if any optician sent him an instrument so defective, he would be
justified in sending it back with the severest censure. But the eye is
not to be judged from the standpoint of theory. It is not perfect,
but is on its way to perfection. As a practical instrument, and taking
the adjustments by which its defects are neutralized into account, it
must ever remain a marvel to the reflecting mind.
§ 3. _Rectilineal Propagation of Light. Elementary Experiments. Law of
Reflection._
The ancients were aware of the rectilineal propagation of light. They
knew that an opaque body, placed between the eye and a point of light,
intercepted the light of the point. Possibly the terms 'ray' and
'beam' may have been suggested by those straight spokes of light
which, in certain states of the atmosphere, dart from the sun at his
rising and his setting. The rectilineal propagation of light may be
illustrated by permitting the solar light to enter, through a small
aperture in a window-shutter, a dark room in which a little smoke has
been diffused. In pure _air_ you cannot see the beam, but in smoky air
you can, because the light, which passes unseen through the air, is
scattered and revealed by the smoke particles, among which the beam
pursues a straight course.
The following instructive experiment depends on the rectilineal
propagation of light. Make a small hole in a closed window-shutter,
before which stands a house or a tree, and place within the darkened
room a white screen at some distance from the orifice. Every straight
ray proceeding from the house, or tree, stamps its colour upon the
screen, and the sum of all the rays will, therefore, be an image of
the object. But, as the rays cross each other at the orifice, the
image is inverted. At present we may illustrate and expand the
subject thus: In front of our camera is a large opening (L, fig. 2),
from which the lens has been removed, and which is closed at present
by a sheet of tin-foil. Pricking by means of a common sewing-needle a
small aperture in the tin-foil, an inverted image of the carbon-points
starts forth upon the screen. A dozen apertures will give a dozen
images, a hundred a hundred, a thousand a thousand. But, as the
apertures come closer to each other, that is to say, as the tin-foil
between the apertures vanishes, the images overlap more and more.
Removing the tin-foil altogether, the screen becomes uniformly
illuminated. Hence the light upon the screen may be regarded as the
overlapping of innumerable images of the carbon-points. In like manner
the light upon every white wall, on a cloudless day, may be regarded
as produced by the superposition of innumerable images of the sun.
[Illustration: Fig. 2.]
The law that the angle of incidence is equal to the angle of
reflection has a bearing upon theory, to be subsequently mentioned,
which renders its simple illustration here desirable. A straight lath
(pointing to the figure 5 on the arc in fig. 3) is fixed as an index
perpendicular to a small looking-glass (M), capable of rotation. We
begin by receiving a beam of light upon the glass which is reflected
back along the line of its incidence. The index being then turned, the
mirror turns with it, and at each side of the index the incident and
the reflected beams (L _o_, _o_ R) track themselves through the dust
of the room. The mere inspection of the two angles enclosed between
the index and the two beams suffices to show their equality; while if
the graduated arc be consulted, the arc from 5 to _m_ is found
accurately equal to the arc from 5 to _n_. The complete expression of
the law of reflection is, not only that the angles of incidence and
reflection are equal, but that the incident and reflected rays always
lie in a plane perpendicular to the reflecting surface.
[Illustration: Fig. 3.]
This simple apparatus enables us to illustrate another law of great
practical importance, namely, that when a mirror rotates, the angular
velocity of a beam reflected from it is twice that of the reflecting
mirror. A simple experiment will make this plain. The arc (_m n_, fig.
3) before you is divided into ten equal parts, and when the incident
beam and the index cross the zero of the graduation, both the incident
and reflected beams are horizontal. Moving the index of the mirror to
1, the reflected beam cuts the arc at 2; moving the index to 2, the
arc is cut at 4; moving the index to 3, the arc is cut at 6; moving
the index at 4, the arc is cut at 8; finally, moving the index to 5,
the arc is cut at 10 (as in the figure). In every case the reflected
beam moves through twice the angle passed over by the mirror.
One of the principal problems of science is to help the senses of man,
by carrying them into regions which could never be attained without
that help. Thus we arm the eye with the telescope when we want to
sound the depths of space, and with the microscope when we want to
explore motion and structure in their infinitesimal dimensions. Now,
this law of angular reflection, coupled with the fact that a beam of
light possesses no weight, gives us the means of magnifying small
motions to an extraordinary degree. Thus, by attaching mirrors to his
suspended magnets, and by watching the images of divided scales
reflected from the mirrors, the celebrated Gauss was able to detect
the slightest thrill of variation on the part of the earth's magnetic
force. By a similar arrangement the feeble attractions and repulsions
of the diamagnetic force have been made manifest. The minute
elongation of a bar of metal, by the mere warmth of the hand, may be
so magnified by this method, as to cause the index-beam to move
through 20 or 30 feet. The lengthening of a bar of iron when it is
magnetized may be also thus demonstrated. Helmholtz long ago employed
this method of rendering evident to his students the classical
experiments of Du Bois Raymond on animal electricity; while in Sir
William Thomson's reflecting galvanometer the principle receives one
of its latest and most important applications.
§ 4. _The Refraction of Light. Total Reflection._
For more than a thousand years no step was taken in optics beyond this
law of reflection. The men of the Middle Ages, in fact, endeavoured,
on the one hand, to develop the laws of the universe _à priori_ out of
their own consciousness, while many of them were so occupied with the
concerns of a future world that they looked with a lofty scorn on all
things pertaining to this one. Speaking of the natural philosophers of
his time, Eusebius says, 'It is not through ignorance of the things
admired by them, but through contempt of their useless labour, that we
think little of these matters, turning our souls to the exercise of
better things.' So also Lactantius--'To search for the causes of
things; to inquire whether the sun be as large as he seems; whether
the moon is convex or concave; whether the stars are fixed in the sky,
or float freely in the air; of what size and of what material are the
heavens; whether they be at rest or in motion; what is the magnitude
of the earth; on what foundations is it suspended or balanced;--to
dispute and conjecture upon such matters is just as if we chose to
discuss what we think of a city in a remote country, of which we never
heard but the name.'
As regards the refraction of light, the course of real inquiry was
resumed in 1100 by an Arabian philosopher named Alhazen. Then it was
taken up in succession by Roger Bacon, Vitellio, and Kepler. One of
the most important occupations of science is the determination, by
precise measurements, of the quantitative relations of phenomena; the
value of such measurements depending greatly upon the skill and
conscientiousness of the man who makes them. Vitellio appears to have
been both skilful and conscientious, while Kepler's habit was to
rummage through the observations of his predecessors, to look at them
in all lights, and thus distil from them the principles which united
them. He had done this with the astronomical measurements of Tycho
Brahe, and had extracted from them the celebrated 'laws of Kepler.' He
did it also with Vitellio's measurements of refraction. But in this
case he was not successful. The principle, though a simple one,
escaped him, and it was first discovered by Willebrord Snell, about
the year 1621.
Less with the view of dwelling upon the phenomenon itself than of
introducing it in a form which will render subsequently intelligible
to you the play of theoretic thought in Newton's mind, the fact of
refraction may be here demonstrated. I will not do this by drawing the
course of the beam with chalk on a black board, but by causing it to
mark its own white track before you. A shallow circular vessel (RIG,
fig. 4), half filled with water, rendered slightly turbid by the
admixture of a little milk, or the precipitation of a little mastic,
is placed with its glass front vertical. By means of a small plane
reflector (M), and through a slit (I) in the hoop surrounding the
vessel, a beam of light is admitted in any required direction. It
impinges upon the water (at O), enters it, and tracks itself through
the liquid in a sharp bright band (O G). Meanwhile the beam passes
unseen through the air above the water, for the air is not competent
to scatter the light. A puff of smoke into this space at once reveals
the track of the incident-beam. If the incidence be vertical, the beam
is unrefracted. If oblique, its refraction at the common surface of
air and water (at O) is rendered clearly visible. It is also seen that
_reflection_ (along O R) accompanies refraction, the beam dividing
itself at the point of incidence into a refracted and a reflected
portion.[4]
[Illustration: Fig. 4.]
The law by which Snell connected together all the measurements
executed up to his time, is this: Let A B C D (fig. 5) represent the
outline of our circular vessel, A C being the water-line. When the
beam is incident along B E, which is perpendicular to A C, there is no
refraction. When it is incident along _m_ E, there is refraction: it
is bent at E and strikes the circle at _n_. When it is incident along
_m'_ E there is also refraction at E, the beam striking the point
_n'_. From the ends of the two incident beams, let the perpendiculars
_m_ _o_, _m'_ _o'_ be drawn upon B D, and from the ends of the
refracted beams let the perpendiculars _p_ _n_, _p'_ _n'_ be also
drawn. Measure the lengths of _o m_ and of _p_ _n_, and divide the one
by the other. You obtain a certain quotient. In like manner divide
_m'_ _o'_ by the corresponding perpendicular _p'_ _n'_; you obtain
precisely the same quotient. Snell, in fact, found this quotient to be
_a constant quantity_ for each particular substance, though it varied
in amount from one substance to another. He called the quotient the
_index of refraction_.
[Illustration Fig. 5]
In all cases where the light is incident from air upon the surface of
a solid or a liquid, or, to speak more generally, when the incidence
is from a less highly refracting to a more highly refracting medium,
the reflection is _partial_. In this case the most powerfully
reflecting substances either transmit or absorb a portion of the
incident light. At a perpendicular incidence water reflects only 18
rays out of every 1,000; glass reflects only 25 rays, while mercury
reflects 666 When the rays strike the surface obliquely the reflection
is augmented. At an incidence of 40°, for example, water reflects 22
rays, at 60° it reflects 65 rays, at 80° 333 rays; while at an
incidence of 89½°, where the light almost grazes the surface, it
reflects 721 rays out of every 1,000. Thus, as the obliquity
increases, the reflection from water approaches, and finally quite
overtakes, the perpendicular reflection from mercury; but at no
incidence, however great, when the incidence is from air, is the
reflection from water, mercury, or any other substance, _total_.
Still, total reflection may occur, and with a view to understanding
its subsequent application in the Nicol's prism, it is necessary to
state when it occurs. This leads me to the enunciation of a principle
which underlies all optical phenomena--the principle of
reversibility.[5] In the case of refraction, for instance, when the
ray passes obliquely from air into water, it is bent _towards_ the
perpendicular; when it passes from water to air, it is bent _from_ the
perpendicular, and accurately reverses its course. Thus in fig. 5, if
_m_ E _n_ be the track of a ray in passing from air into water, _n_ E
_m_ will be its track in passing from water into air. Let us push this
principle to its consequences. Supposing the light, instead of being
incident along _m_ E or _m'_ E, were incident as close as possible
along C E (fig. 6); suppose, in other words, that it just grazes the
surface before entering the water. After refraction it will pursue
say the course E _n_''. Conversely, if the light start from _n_'', and
be incident at E, it will, on escaping into the air, just graze the
surface of the water. The question now arises, what will occur
supposing the ray from the water to follow the course _n_''' E, which
lies beyond _n_'' E? The answer is, it will not quit the water at all,
but will be _totally_ reflected (along E _x_). At the under surface of
the water, moreover, the law is just the same as at its upper surface,
the angle of incidence (D E _n_''') being equal to the angle of
reflection (D E _x_).
[Illustration: Fig. 6]
Total reflection may be thus simply illustrated:--Place a shilling in
a drinking-glass, and tilt the glass so that the light from the
shilling shall fall with the necessary obliquity upon the water
surface above it. Look upwards through the water towards that surface,
and you see the image of the shilling shining there as brightly as the
shilling itself. Thrust the closed end of an empty test-tube into
water, and incline the tube. When the inclination is sufficient,
horizontal light falling upon the tube cannot enter the air within it,
but is totally reflected upward: when looked down upon, such a tube
looks quite as bright as burnished silver. Pour a little water into
the tube; as the liquid rises, total reflection is abolished, and with
it the lustre, leaving a gradually diminishing shining zone, which
disappears wholly when the level of the water within the tube reaches
that without it. Any glass tube, with its end stopped water-tight,
will produce this effect, which is both beautiful and instructive.
Total reflection never occurs except in the attempted passage of a ray
from a more refracting to a less refracting medium; but in this case,
when the obliquity is sufficient, it always occurs. The mirage of the
desert, and other phantasmal appearances in the atmosphere, are in
part due to it. When, for example, the sun heats an expanse of sand,
the layer of air in contact with the sand becomes lighter and less
refracting than the air above it: consequently, the rays from a
distant object, striking very obliquely on the surface of the heated
stratum, are sometimes totally reflected upwards, thus producing
images similar to those produced by water. I have seen the image of a
rock called Mont Tombeline distinctly reflected from the heated air of
the strand of Normandy near Avranches; and by such delusive
appearances the thirsty soldiers of the French army in Egypt were
greatly tantalised.
The angle which marks the limit beyond which total reflection takes
place is called the _limiting angle_ (it is marked in fig. 6 by the
strong line E _n_''). It must evidently diminish as the refractive
index increases. For water it is 48½°, for flint glass 38°41', and for
diamond 23°42'. Thus all the light incident from two complete
quadrants, or 180°, in the case of diamond, is condensed into an
angular space of 47°22' (twice 23°42') by refraction. Coupled with its
great refraction, are the great dispersive and great reflective
powers of diamond; hence the extraordinary radiance of the gem, both
as regards white light and prismatic light.
§ 5. _Velocity of Light. Aberration. Principle of least Action._
In 1676 a great impulse was given to optics by astronomy. In that year
Olav Roemer, a learned Dane, was engaged at the Observatory of Paris
in observing the eclipses of Jupiter's moons. The planet, whose
distance from the sun is 475,693,000 miles, has four satellites. We
are now only concerned with the one nearest to the planet. Roemer
watched this moon, saw it move round the planet, plunge into Jupiter's
shadow, behaving like a lamp suddenly extinguished: then at the other
edge of the shadow he saw it reappear, like a lamp suddenly lighted.
The moon thus acted the part of a signal light to the astronomer, and
enabled him to tell exactly its time of revolution. The period between
two successive lightings up of the lunar lamp he found to be 42 hours,
28 minutes, and 35 seconds.
This measurement of time was so accurate, that having determined the
moment when the moon emerged from the shadow, the moment of its
hundredth appearance could also be determined. In fact, it would be
100 times 42 hours, 28 minutes, 35 seconds, after the first
observation.
Roemer's first observation was made when the earth was in the part of
its orbit nearest Jupiter. About six months afterwards, the earth
being then at the opposite side of its orbit, when the little moon
ought to have made its hundredth appearance, it was found unpunctual,
being fully 15 minutes behind its calculated time. Its appearance,
moreover, had been growing gradually later, as the earth retreated
towards the part of its orbit most distant from Jupiter. Roemer
reasoned thus: 'Had I been able to remain at the other side of the
earth's orbit, the moon might have appeared always at the proper
instant; an observer placed there would probably have seen the moon 15
minutes ago, the retardation in my case being due to the fact that the
light requires 15 minutes to travel from the place where my first
observation was made to my present position.'
This flash of genius was immediately succeeded by another. 'If this
surmise be correct,' Roemer reasoned, 'then as I approach Jupiter
along the other side of the earth's orbit, the retardation ought to
become gradually less, and when I reach the place of my first
observation, there ought to be no retardation at all.' He found this
to be the case, and thus not only proved that light required time to
pass through space, but also determined its rate of propagation.
The velocity of light, as determined by Roemer, is 192,500 miles in a
second.
For a time, however, the observations and reasonings of Roemer failed
to produce conviction. They were doubted by Cassini, Fontenelle, and
Hooke. Subsequently came the unexpected corroboration of Roemer by the
English astronomer, Bradley, who noticed that the fixed stars did not
really appear to be fixed, but that they describe little orbits in the
heavens every year. The result perplexed him, but Bradley had a mind
open to suggestion, and capable of seeing, in the smallest fact, a
picture of the largest. He was one day upon the Thames in a boat, and
noticed that as long as his course remained unchanged, the vane upon
his masthead showed the wind to be blowing constantly in the same
direction, but that the wind appeared to vary with every change in the
direction of his boat. 'Here,' as Whewell says, 'was the image of his
case. The boat was the earth, moving in its orbit, and the wind was
the light of a star.'
We may ask, in passing, what, without the faculty which formed the
'image,' would Bradley's wind and vane have been to him? A wind and
vane, and nothing more. You will immediately understand the meaning of
Bradley's discovery. Imagine yourself in a motionless railway-train,
with a shower of rain descending vertically downwards. The moment the
train begins to move, the rain-drops begin to slant, and the quicker
the motion of the train the greater is the obliquity. In a precisely
similar manner the rays from a star, vertically overhead, are caused
to slant by the motion of the earth through space. Knowing the speed
of the train, and the obliquity of the falling rain, the velocity of
the drops may be calculated; and knowing the speed of the earth in her
orbit, and the obliquity of the rays due to this cause, we can
calculate just as easily the velocity of light. Bradley did this, and
the 'aberration of light,' as his discovery is called, enabled him to
assign to it a velocity almost identical with that deduced by Roemer
from a totally different method of observation. Subsequently Fizeau,
and quite recently Cornu, employing not planetary or stellar
distances, but simply the breadth of the city of Paris, determined the
velocity of light: while Foucault--a man of the rarest mechanical
genius--solved the problem without quitting his private room. Owing
to an error in the determination of the earth's distance from the sun,
the velocity assigned to light by both Roemer and Bradley is too
great. With a close approximation to accuracy it may be regarded as
186,000 miles a second.
By Roemer's discovery, the notion entertained by Descartes, and
espoused by Hooke, that light is propagated instantly through space,
was overthrown. But the establishment of its motion through stellar
space led to speculations regarding its velocity in transparent
terrestrial substances. The 'index of refraction' of a ray passing
from air into water is 4/3. Newton assumed these numbers to mean that
the velocity of light in water being 4, its velocity in air is 3; and
he deduced the phenomena of refraction from this assumption. Huyghens
took the opposite and truer view. According to this great man, the
velocity of light in water being 3, its velocity in air is 4; but both
in Newton's time and ours the same great principle determined, and
determines, the course of light in all cases. In passing from point to
point, whatever be the media in its path, or however it may be
refracted or reflected, light takes the course which occupies _least
time_. Thus in fig. 4, taking its velocity in air and in water into
account, the light reaches G from I more rapidly by travelling first
to O, and there changing its course, than if it proceeded straight
from I to G. This is readily comprehended, because, in the latter
case, it would pursue a greater distance through the water, which is
the more retarding medium.
§ 6. _Descartes' Explanation of the Rainbow_.
Snell's law of refraction is one of the corner-stones of optical
science, and its applications to-day are million-fold. Immediately
after its discovery Descartes applied it to the explanation of the
rainbow. A beam of solar light falling obliquely upon a rain-drop is
refracted on entering the drop. It is in part reflected at the back of
the drop, and on emerging it is again refracted. By these two
refractions, and this single reflection, the light is sent to the eye
of an observer facing the drop, and with his back to the sun.
Conceive a line drawn from the sun, through the back of his head, to
the observer's eye and prolonged beyond it. Conceive a second line
drawn from the shower to the eye, and enclosing an angle of 42½° with
the line drawn from the sun. Along this second line a rain-drop when
struck by a sunbeam will send red light to the eye. Every other drop
similarly situated, that is, every drop at an angular distance of 42½°
from the line through the sun and eye, will do the same. A circular
band of red light is thus formed, which may be regarded as the
boundary of the base of a cone, with its apex at the observer's eye.
Because of the magnitude of the sun, the angular width of this red
band will be half a degree.
From the eye of the observer conceive another line to be drawn,
enclosing an angle, not of 42½°, but of 40½°, with the prolongation of
the line drawn from the sun. Along this other line a rain-drop, at its
remote end, when struck by a solar beam, will send violet light to the
eye. All drops at the same angular distance will do the same, and we
shall therefore obtain a band of violet light of the same width as the
red band. These two bands constitute the limiting colours of the
rainbow, and between them the bands corresponding to the other colours
lie.
Thus the line drawn from the eye to the _middle_ of the bow, and the
line drawn through the eye to the sun, always enclose an angle of
about 41°. To account for this was the great difficulty, which
remained unsolved up to the time of Descartes.
Taking a pen in hand, and calculating by means of Snell's law the
track of every ray through a raindrop, Descartes found that, at one
particular angle, the rays, reflected at its back, emerged from the
drop _almost parallel to each other_. They were thus enabled to
preserve their intensity through long atmospheric distances. At all
other angles the rays quitted the drop _divergent_, and through this
divergence became so enfeebled as to be practically lost to the eye.
The angle of parallelism here referred to was that of forty-one
degrees, which observation had proved to be invariably associated with
the rainbow.
From what has been said, it is clear that two observers standing
beside each other, or one above the other, nay, that even the two eyes
of the same observer, do not see exactly the same bow. The position of
the base of the cone changes with that of its apex. And here we have
no difficulty in answering a question often asked--namely, whether a
rainbow is ever seen reflected in water. Seeing two bows, the one in
the heavens, the other in the water, you might be disposed to infer
that the one bears the same relation to the other that a tree upon the
water's edge bears to its reflected image. The rays, however, which
reach an observer's eye after reflection from the water, and which
form a bow in the water, would, were their course from the shower
uninterrupted, converge to a point vertically under the observer, and
as far below the level of the water as his eye is above it. But under
no circumstances could an eye above the water-level and one below it
see the same bow--in other words, the self-same drops of rain cannot
form the reflected bow and the bow seen directly in the heavens. The
reflected bow, therefore, is not, in the usual optical sense of the
term, the _image_ of the bow seen in the sky.
§ 7. _Analysis and Synthesis of Light. Doctrine of Colours_.
In the rainbow a new phenomenon was introduced--the phenomenon of
colour. And here we arrive at one of those points in the history of
science, when great men's labours so intermingle that it is difficult
to assign to each worker his precise meed of honour. Descartes was at
the threshold of the discovery of the composition of solar light; but
for Newton was reserved the enunciation of the true law. He went to
work in this way: Through the closed window-shutter of a room he
pierced an orifice, and allowed a thin sunbeam to pass through it. The
beam stamped a round white image of the sun on the opposite wall of
the room. In the path of this beam Newton placed a prism, expecting to
see the beam refracted, but also expecting to see the image of the
sun, after refraction, still round. To his astonishment, it was drawn
out to an image with a length five times its breadth. It was,
moreover, no longer white, but divided into bands of different
colours. Newton saw immediately that solar light was _composite_, not
simple. His elongated image revealed to him the fact that some
constituents of the light were more deflected by the prism than
others, and he concluded, therefore, that white light was a mixture of
lights of different colours, possessing different degrees of
refrangibility.
Let us reproduce this celebrated experiment. On the screen is now
stamped a luminous disk, which may stand for Newton's image of the
sun. Causing the beam (from the aperture L, fig. 7) which produces the
disk to pass through a lens (E), we form a sharp image of the
aperture. Placing in the track of the beam a prism (P), we obtain
Newton's coloured image, with its red and violet ends, which he called
a _spectrum_. Newton divided the spectrum into seven parts--red,
orange, yellow, green, blue, indigo, violet; which are commonly called
the seven primary or prismatic colours. The drawing out of the white
light into its constituent colours is called _dispersion_.
[Illustration: Fig. 7.]
This was the first _analysis_ of solar light by Newton; but the
scientific mind is fond of verification, and never neglects it where
it is possible. Newton completed his proof by _synthesis_ in this way:
The spectrum now before you is produced by a glass prism. Causing the
decomposed beam to pass through a second similar prism, but so placed
that the colours are refracted back and reblended, the perfectly white
luminous disk is restored.
[Illustration: Fig. 8.]
In this case, refraction and dispersion are simultaneously abolished.
Are they always so? Can we have the one without the other? It was
Newton's conclusion that we could not. Here he erred, and his error,
which he maintained to the end of his life, retarded the progress of
optical discovery. Dollond subsequently proved that by combining two
different kinds of glass, the colours can be extinguished, still
leaving a residue of refraction, and he employed this residue in the
construction of achromatic lenses--lenses yielding no colour--which
Newton thought an impossibility. By setting a water-prism--water
contained in a wedge-shaped vessel with glass sides (B, fig. 8)--in
opposition to a wedge of glass (to the right of B), this point can be
illustrated before you. We have first of all the position (dotted) of
the unrefracted beam marked upon the screen; then we produce the
narrow water-spectrum (W); finally, by introducing a flint-glass
prism, we refract the beam back, until the colour disappears (at A).
The image of the slit is now _white_; but though the dispersion is
abolished, there remains a very sensible amount of refraction.
This is the place to illustrate another point bearing upon the
instrumental means employed in these lectures. Bodies differ widely
from each other as to their powers of refraction and dispersion. Note
the position of the water-spectrum upon the screen. Altering in no
particular the wedge-shaped vessel, but simply substituting for the
water the transparent bisulphide of carbon, you notice how much higher
the beam is thrown, and how much richer is the display of colour. To
augment the size of our spectrum we here employ (at L) a slit, instead
of a circular aperture.[6]
[Illustration: Fig. 9.]