is more sluggish than in the other; and, as a consequence, the waves
that follow this direction are more retarded than the others. In both
cases the undulations are shortened when they enter the gypsum, but
in the one case they are more shortened than in the other. You can
readily imagine that in this way the one system of waves may get half
a wave-length, or indeed any number of half wavelengths, in advance of
the other. The possibility of interference here at once flashes upon
the mind. A little consideration, however, will render it evident
that, as long as the vibrations are executed at right angles to each
other, they cannot quench each other, no matter what the retardation
may be. This brings us at once to the part played by the analyzer. Its
sole function is to recompound the two vibrations emergent from the
gypsum. It reduces them to a single plane, where, if one of them be
retarded by the proper amount, extinction will occur.
But here, as in the case of thin films, the different lengths of the
waves of light come into play. Red will require a greater thickness to
produce the retardation necessary for extinction than blue;
consequently when the longer waves have been withdrawn by
interference, the shorter ones remain, the film of gypsum shining with
the colours which the short waves confer. Conversely, when the shorter
waves have been withdrawn, the thickness is such that the longer waves
remain. An elementary consideration suffices to show, that when the
directions of vibration of the prisms and the gypsum enclose an angle
of forty-five degrees, the colours are at their maximum brilliancy.
When the film is turned from this direction, the colours gradually
fade, until, at the point where the directions of vibration in plate
and prisms are parallel, they disappear altogether.
(The best way of obtaining a knowledge of these phenomena is to
construct a model of thin wood or pasteboard, representing the plate
of gypsum, its planes of vibration, and also those of the polarizer
and analyzer. Two parallel pieces of the board are to be separated by
an interval which shall represent the thickness of the film of gypsum.
Between them two other pieces, intersecting each other at a right
angle, are to represent the planes of vibration within the film; while
attached to the two parallel surfaces outside are two other pieces of
board, which represent the planes of vibration of the polarizer and
analyzer. On the two intersecting planes the waves are to be drawn,
showing the resolution of the first polarized beam into two others,
and then the subsequent reduction of the two systems of vibrations to
a common plane by the analyzer. Following out rigidly the interaction
of the two systems of waves, we are taught by such a model that all
the phenomena of colour obtained by the combination of the waves, when
the planes of vibration of the two Nicols are parallel, are displaced
by the _complementary_ phenomena, when the planes of vibration are
perpendicular to each other.)
In considering the next point, we will operate, for the sake of
simplicity, with monochromatic light--with red light, for example,
which is easily obtained pure by red glass. Supposing a certain
thickness of the gypsum produces a retardation of half a wave-length,
twice this thickness will produce a retardation of two half
wave-lengths, three times this thickness a retardation of three half
wave-lengths, and so on. Now, when the Nicols are parallel, the
retardation of half a wave-length, or of any _odd_ number of half
wave-lengths, produces extinction; at all thicknesses, on the other
hand, which correspond to a retardation of an _even_ number of half
wave-lengths, the two beams support each other, when they are brought
to a common plane by the analyzer. Supposing, then, that we take a
plate of a wedge form, which grows gradually thicker from edge to
back, we ought to expect, in red light, a series of recurrent bands of
light and darkness; the dark bands occurring at thicknesses which
produce retardations of one, three, five, etc., half wave-lengths,
while the bright bands occur between the dark ones. Experiment proves
the wedge-shaped film to show these bands. They are also beautifully
shown by a circular film, so worked as to be thinnest at the centre,
and gradually increasing in thickness from the centre outwards. A
splendid series of rings of light and darkness is thus produced.
When, instead of employing red light, we employ blue, the rings are
also seen: but as they occur at thinner portions of the film, they are
smaller than the rings obtained with the red light. The consequence of
employing white light may be now inferred; inasmuch as the red and the
blue fall in different places, we have _iris-coloured_ rings produced
by the white light.
Some of the chromatic effects of irregular crystallization are
beautiful in the extreme. Could I introduce between our two Nicols a
pane of glass covered by those frost-ferns which your cold weather
renders now so frequent, rich colours would be the result. The
beautiful effects of the irregular crystallization of tartaric acid
and other substances on glass plates now presented to you, illustrate
what you might expect from the frosted window-pane. And not only do
crystalline bodies act thus upon light, but almost all bodies that
possess a definite structure do the same. As a general rule, organic
bodies act thus upon light; for their architecture implies an
arrangement of the molecules, and of the ether associated with the
molecules, which involves double refraction. A film of horn, or the
section of a shell, for example, yields very beautiful colours in
polarized light. In a tree, the ether certainly possesses different
degrees of elasticity along and across the fibre; and, were wood
transparent, this peculiarity of molecular structure would infallibly
reveal itself by chromatic phenomena like those that you have seen.
§ 4. _Colours produced by Strain and Pressure._
Not only do natural bodies behave in this way, but it is possible, as
shown by Brewster, to confer, by artificial strain or pressure, a
temporary double refracting structure upon non-crystalline bodies such
as common glass. This is a point worthy of illustration. When I place
a bar of wood across my knee and seek to break it, what is the
mechanical condition of the bar? It bends, and its convex surface is
_strained_ longitudinally; its concave surface, that next my knee, is
longitudinally _pressed_. Both in the strained portion and in the
pressed portion of the wood the ether is thrown into a condition which
would render the wood, were it transparent, double-refracting. For, in
cases like the present, the drawing of the molecules asunder
longitudinally is always accompanied by their approach to each other
laterally; while the longitudinal squeezing is accompanied by lateral
retreat. Each half of the bar of wood exhibits this antithesis, and is
therefore double-refracting.
Let us now repeat this experiment with a bar of glass. Between the
crossed Nicols I introduce such a bar. By the dim residue of light
lingering upon the screen, you see the image of the glass, but it has
no effect upon the light. I simply bend the glass bar with my finger
and thumb, keeping its length oblique to the directions of vibration
in the Nicols. Instantly light flashes out upon the screen. The two
sides of the bar are illuminated, the edges most, for here the strain
and pressure are greatest. In passing from longitudinal strain to
longitudinal pressure, we cross a portion of the glass where neither
is exerted. This is the so-called neutral axis of the bar of glass,
and along it you see a dark band, indicating that the glass along this
axis exercises no action upon the light. By employing the force of a
press, instead of the force of my finger and thumb, the brilliancy of
the light is greatly augmented.
Again, I have here a square of glass which can be inserted into a
press of another kind. Introducing the uncompressed square between the
prisms, its neutrality is declared; but it can hardly be held
sufficiently loosely in the press to prevent its action from
manifesting itself. Already, though the pressure is infinitesimal, you
see spots of light at the points where the press is in contact with
the glass. On turning a screw, the image of the square of glass
flashes out upon the screen. Luminous spaces are seen separated from
each other by dark bands.
Every two adjacent spaces are in opposite mechanical conditions. On
one side of the dark band we have strain, on the other side pressure,
the band marking the neutral axis between both. I now tighten the
vice, and you see colour; tighten still more, and the colours appear
as rich as those presented by crystals. Releasing the vice, the
colours suddenly vanish; tightening suddenly, they reappear. From the
colours of a soap-bubble Newton was able to infer the thickness of the
bubble, thus uniting by the bond of thought apparently incongruous
things. From the colours here presented to you, the magnitude of the
pressure employed might be inferred. Indeed, the late M. Wertheim, of
Paris, invented an instrument for the determination of strains and
pressures, by the colours of polarized light, which exceeded in
accuracy all previous instruments of the kind.
And now we have to push these considerations to a final illustration.
Polarized light may be turned to account in various ways as an
analyzer of molecular condition. It may, for instance, be applied to
reveal the condition of a solid body when it becomes sonorous. A strip
of glass six feet long, two inches wide and a quarter of an inch
thick, is held at the centre between the finger and thumb. On sweeping
a wet woollen rag over one of its halves, you hear an acute sound due
to the vibrations of the glass. What is the condition of the glass
while the sound is heard? This: its two halves lengthen and shorten in
quick succession. Its two ends, therefore, are in a state of quick
vibration; but at the centre the pulses from the two ends alternately
meet and retreat from each other. Between their opposing actions, the
glass at the centre is kept motionless: but, on the other hand, it is
alternately strained and compressed. In fig. 38, A B may be taken to
represent the glass rectangle with its centre condensed; while A' B'
represents the same rectangle with its centre rarefied. The ends of
the strip suffer neither condensation nor rarefaction.
[Illustration: Fig. 38]
If we introduce the strip of glass (_s_ _s'_, fig. 39) between the
crossed Nicols, taking care to keep it oblique to the directions of
vibration of the Nicols, and sweep our wet rubber over the glass, this
is what may be expected to occur: At every moment of compression the
light will flash through; at every moment of strain the light will
also flash through; and these states of strain and pressure will
follow each other so rapidly, that we may expect a permanent luminous
impression to be made upon the eye. By pure reasoning, therefore, we
reach the conclusion that the light will be revived whenever the glass
is sounded. That it is so, experiment testifies: at every sweep of the
rubber (_h_, fig. 39) a fine luminous disk (O) flashes out upon the
screen. The experiment may be varied in this way: Placing in front of
the polarizer a plate of unannealed glass, you have a series of
beautifully coloured rings, intersected by a black cross. Every sweep
of the rubber not only abolishes the rings, but introduces
complementary ones, the black cross being, for the moment, supplanted
by a white one. This is a modification of a beautiful experiment which
we owe to Biot. His apparatus, however, confined the observation of it
to a single person at a time.
[Illustration: Fig. 39.]
§ 5. _Colours of Unannealed Glass_.
Bodies are usually expanded by heat and contracted by cold. If the
heat be applied with perfect uniformity, no local strains or pressures
come into play; but, if one portion of a solid be heated and another
portion not, the expansion of the heated portion introduces strains
and pressures which reveal themselves under the scrutiny of polarized
light. When a square of common window-glass is placed between the
Nicols, you see its dim outline, but it exerts no action on the
polarized light. Held for a moment over the flame of a spirit-lamp, on
reintroducing it between the Nicols, light flashes out upon the
screen. Here, as in the case of mechanical action, you have luminous
spaces of strain divided by dark neutral axes from spaces of pressure.
[Illustration: Fig. 40.]
[Illustration: Fig. 41.]
Let us apply the heat more symmetrically. A small square of glass is
perforated at the centre, and into the orifice a bit of copper wire is
introduced. Placing the square between the prisms, and heating the
wire, the heat passes by conduction to the glass, through which it
spreads from the centre outwards. You immediately see four luminous
quadrants and a dim cross, which becomes gradually blacker, by
comparison with the adjacent brightness. And as, in the case of
pressure, we produced colours, so here also, by the proper application
of heat, gorgeous chromatic effects may be evoked. The condition
necessary to the production of these colours may be rendered permanent
by first heating the glass sufficiently, and then cooling it, so that
the chilled mass shall remain in a state of permanent strain and
pressure. Two or three examples will illustrate this point. Figs. 40
and 41 represent the figures obtained with two pieces of glass thus
prepared; two rectangular pieces of unannealed glass, crossed and
placed between the polarizer and analyzer, exhibit the beautiful iris
fringes represented in fig. 42.
[Illustration: Fig. 42.]
§ 6. _Circular Polarization._
But we have to follow the ether still further into its hiding-places.
Suspended before you is a pendulum, which, when drawn aside and
liberated, oscillates to and fro. If, when the pendulum is passing the
middle point of its excursion, I impart a shock to it tending to drive
it at right angles to its present course, what occurs? The two
impulses compound themselves to a vibration oblique in direction to
the former one, but the pendulum still oscillates in _a plane_. But,
if the rectangular shock be imparted to the pendulum when it is at the
limit of its swing, then the compounding of the two impulses causes
the suspended ball to describe, not a straight line, but an ellipse;
and, if the shock be competent of itself to produce a vibration of the
same amplitude as the first one, the ellipse becomes a circle.
Why do I dwell upon these things? Simply to make known to you the
resemblance of these gross mechanical vibrations to the vibrations of
light. I hold in my hand a plate of quartz cut from the crystal
perpendicular to its axis. The crystal thus cut possesses the
extraordinary power of twisting the plane of vibration of a polarized
ray to an extent dependent on the thickness of the crystal. And the
more refrangible the light the greater is the amount of twisting; so
that, when white light is employed, its constituent colours are thus
drawn asunder. Placing the quartz plate between the polarizer and
analyzer, this vivid red appears; and, turning the analyzer in front
from right to left, the other colours of the spectrum appear in
succession. Specimens of quartz have been found which require the
analyzer to be turned from left to right to obtain the same succession
of colours. Crystals of the first class are therefore called
right-handed, and of the second class, left-handed crystals.
With profound sagacity, Fresnel, to whose genius we mainly owe the
expansion and final triumph of the undulatory theory of light,
reproduced mentally the mechanism of these crystals, and showed their
action to be due to the circumstance that, in them, the waves of
ether so act upon each other as to produce the condition represented
by our rotating pendulum. Instead of being plane polarized, the light
in rock crystal is _circularly polarized_. Two such rays, transmitted
along the axis of the crystal, and rotating in opposite directions,
when brought to interference by the analyzer, are demonstrably
competent to produce all the observed phenomena.
§ 7. _Complementary Colours of Bi-refracting Spar in Circularly
Polarized Light. Proof that Yellow and Blue are Complementary._
I now remove the analyzer, and put in its place the piece of Iceland
spar with which we have already illustrated double refraction. The two
images of the carbon-points are now before you, produced, as you know,
by two beams vibrating at right angles to each other. Introducing a
plate of quartz between the polarizer and the spar, the two images
glow with complementary colours. Employing the image of an aperture
instead of that of the carbon-points, we have two coloured circles. As
the analyzer is caused to rotate, the colours pass through various
changes: but they are always complementary. When the one is red, the
other is green; when the one is yellow, the other is blue. Here we
have it in our power to demonstrate afresh a statement made in our
first lecture, that although the mixture of blue and yellow pigments
produces green, the mixture of blue and yellow lights produces white.
By enlarging our aperture, the two images produced by the spar are
caused to approach each other, and finally to overlap. The one image
is now a vivid yellow, the other a vivid blue, and you notice that
where these colours are superposed we have a pure white. (See fig. 43,
where N is the end of the polarizer, Q the quartz plate, L a lens, and
B the bi-refracting spar. The two images overlap at O, and produce
white by their mixture.)
[Illustration: Fig. 43.]
§ 8. _The Magnetization of Light._
This brings us to a point of our inquiries which, though rarely
illustrated in lectures, is nevertheless so likely to affect
profoundly the future course of scientific thought that I am unwilling
to pass it over without reference. I refer to the experiment which
Faraday, its discoverer, called the 'magnetization of light.' The
arrangement for this celebrated experiment is now before you. We have,
first, our electric lamp, then a Nicol prism, to polarize the beam
emergent from the lamp; then an electro-magnet, then a second Nicol,
and finally our screen. At the present moment the prisms are crossed,
and the screen is dark. I place from pole to pole of the
electro-magnet a cylinder of a peculiar kind of glass, first made by
Faraday, and called Faraday's heavy glass. Through this glass the beam
from the polarizer now passes, being intercepted by the Nicol in
front. On exciting the magnet light instantly appears upon the screen.
By the action of the magnet upon the heavy glass the plane of
vibration is caused to rotate, the light being thus enabled to get
through the analyzer.
The two classes into which quartz-crystals are divided have been
already mentioned. In my hand I hold a compound plate, one half of it
taken from a right-handed, and the other from a left-handed crystal.
Placing the plate in front of the polarizer, I turn one of the Nicols
until the two halves of the plate show a common puce colour. This
yields an exceedingly sensitive means of rendering visible the action
of a magnet upon light. By turning either the polarizer or the
analyzer through the smallest angle, the uniformity of the colour
disappears, and the two halves of the quartz show different colours.
The magnet produces an effect equivalent to this rotation. The
puce-coloured circle is now before you on the screen. (See fig. 44,
where N is the nozzle of the lamp, H the first Nicol, Q the biquartz
plate, L a lens, M the electro-magnet, with the heavy glass across its
perforated poles, and P the second Nicol.) Exciting the magnet, one
half of the image becomes suddenly red, the other half green.
Interrupting the current, the two colours fade away, and the primitive
puce is restored.
The action, moreover, depends upon the polarity of the magnet, or, in
other words, on the direction of the current which surrounds the
magnet. Reversing the current, the red and green reappear, but they
have changed places. The red was formerly to the right, and the green
to the left; the green is now to the right, and the red to the left.
With the most exquisite ingenuity, Faraday analyzed all those actions
and stated their laws. This experiment, however, long remained a
scientific curiosity rather than a fruitful germ. That it would bear
fruit of the highest importance, Faraday felt profoundly convinced,
and present researches are on the way to verify his conviction.
[Illustration: Fig. 44]
§ 9. _Iris-rings surrounding the Axes of Crystals._
A few more words are necessary to complete our knowledge of the
wonderful interaction between ponderable molecules and the ether
interfused among them. Symmetry of molecular arrangement implies
symmetry on the part of the ether; atomic dissymmetry, on the other
hand, involves the dissymmetry of the ether, and, as a consequence,
double refraction. In a certain class of crystals the structure is
homogeneous, and such crystals produce no double refraction. In
certain other crystals the molecules are ranged symmetrically round a
certain line, and not around others. Along the former, therefore, the
ray is undivided, while along all the others we have double
refraction. Ice is a familiar example: its molecules are built with
perfect symmetry around the perpendiculars to the planes of freezing,
and a ray sent through ice in this direction is not doubly refracted;
whereas, in all other directions, it is. Iceland spar is another
example of the same kind: its molecules are built symmetrically round
the line uniting the two blunt angles of the rhomb. In this direction
a ray suffers no double refraction, in all others it does. This
direction of no double refraction is called the _optic axis_ of the
crystal.
Hence, if a plate be cut from a crystal of Iceland spar perpendicular
to the axis, all rays sent across this plate in the direction of the
axis will produce but one image. But, the moment we deviate from the
parallelism with the axis, double refraction sets in. If, therefore, a
beam that has been rendered _conical_ by a converging lens be sent
through the spar so that the central ray of the cone passes along the
axis, this ray only will escape double refraction. Each of the others
will be divided into an ordinary and an extraordinary ray, the one
moving more slowly through the crystal than the other; the one,
therefore, retarded with reference to the other. Here, then, we have
the conditions for interference, when the waves are reduced by the
analyzer to a common plane.
Placing the plate of Iceland spar between the crossed Nicol prisms,
and employing the conical beam, we have upon the screen a beautiful
system of iris-rings surrounding the end of the optic axis, the
circular bands of colour being intersected by a black cross (fig. 45).
The arms of this cross are parallel to the two directions of vibration
in the polarizer and analyzer. It is easy to see that those rays whose
planes of vibration within the spar coincide with the plane of
vibration of _either_ prism, cannot get through _both_. This complete
interception produces the arms of the cross.
[Illustration: Fig. 45.]
With monochromatic light the rings would be simply bright and
black--the bright rings occurring at those thicknesses of the spar
which cause the rays to conspire; the black rings at those thicknesses
which cause them to quench each other. Turning the analyzer 90° round,
we obtain the complementary phenomena. The black cross gives place to
a bright one, and every dark ring is supplanted also by a bright one
(fig. 46). Here, as elsewhere, the different lengths of the
light-waves give rise to iris-colours when white light is employed.
[Illustration: Fig. 46.]
[Illustration: Fig. 47.]
Besides the _regular_ crystals which produce double refraction in no
direction, and the _uniaxal_ crystals which produce it in all
directions but one, Brewster discovered that in a large class of
crystals there are _two_ directions in which double refraction does
not take place. These are called _biaxal_ crystals. When plates of
these crystals, suitably cut, are placed between the polarizer and
analyzer, the axes (A A', fig. 47) are seen surrounded, not by
circles, but by curves of another order and of a perfectly definite
mathematical character. Each band, as proved experimentally by
Herschel, forms a _lemniscata_; but the experimental proof was here,
as in numberless other cases, preceded by the deduction which showed
that, according to the undulatory theory, the bands must possess this
special character.
§ 10. _Power of the Wave Theory_.