Polarization of Light—Defined—Polarization by Refraction—Properties of
the Tourmaline—Double Refraction—All doubly Refracted Light is
Polarized—Properties of Iceland Spar—Tourmaline absorbs one of the two
Refracted Rays—Undulations of Natural Light—Undulations of Polarized
Light—The Optic Axes of Crystals—M. Fresnel’s Discoveries on the Rays
passing along the Optic Axis—Polarization by Reflection.
IN giving a sketch of the constitution of light, it is impossible to
omit the extraordinary property of its polarization, “the phenomena of
which,” Sir John Herschel says, “are so singular and various, that to
one who has only studied the common branches of physical optics it is
like entering into a new world, so splendid as to render it one of the
most delightful branches of experimental inquiry, and so fertile in the
views it lays open of the constitution of natural bodies, and the
minuter mechanism of the universe, as to place it in the very first rank
of the physico-mathematical sciences, which it maintains by the rigorous
application of geometrical reasoning its nature admits and requires.”
Light is said to be polarized, which, by being once reflected or
refracted, is rendered incapable of being again reflected or refracted
at certain angles. In general, when a ray of light is reflected from a
pane of plate-glass, or any other substance, it may be reflected a
second time from another surface, and it will also pass freely through
transparent bodies. But, if a ray of light be reflected from a pane of
plate-glass at an angle of 57°, it is rendered totally incapable of
reflection at the surface of another pane of glass in certain definite
positions, but it will be completely reflected by the second pane in
other positions. It likewise loses the property of penetrating
transparent bodies in particular positions, whilst it is freely
transmitted by them in others. Light, so modified as to be incapable of
reflection and transmission in certain directions, is said to be
polarized.
Light may be polarized by reflection from any polished surface, and the
same property is also imparted by refraction. It is proposed to explain
these methods of polarizing light, to give a short account of its most
remarkable properties, and to endeavour to describe a few of the
splendid phenomena it exhibits.
If a brown tourmaline, which is a mineral generally crystallized in the
form of a long prism, be cut longitudinally, that is, parallel to the
axis of the prism, into plates about the thirtieth of an inch in
thickness, and the surfaces polished, luminous objects may be seen
through them, as through plates of coloured glass. The axis of each
plate is in its longitudinal section parallel to the axis of the prism
whence it was cut (N. 204). If one of these plates be held
perpendicularly between the eye and a candle, and turned slowly round in
its own plane, no change will take place in the image of the candle. But
if the plate be held in a fixed position, with its axis or longitudinal
section vertical, when a second plate of tourmaline is interposed
between it and the eye, parallel to the first, and turned slowly round
in its own plane, a remarkable change will be found to have taken place
in the nature of the light. For the image of the candle will vanish and
appear alternately at every quarter revolution of the plate, varying
through all degrees of brightness down to total or almost total
evanescence, and then increasing again by the same degrees as it had
before decreased. These changes depend upon the relative positions of
the plates. When the longitudinal sections of the two plates are
parallel, the brightness of the image is at its maximum; and, when the
axes of the sections cross at right angles, the image of the candle
vanishes. Thus the light, in passing through the first plate of
tourmaline, has acquired a property totally different from the direct
light of the candle. The direct light would have penetrated the second
plate equally well in all directions, whereas the refracted ray will
only pass through it in particular positions, and is altogether
incapable of penetrating it in others. The refracted ray is polarized in
its passage through the first tourmaline, and experience shows that it
never loses that property, unless when acted upon by a new substance.
Thus, one of the properties of polarized light is the incapability of
passing through a plate of tourmaline perpendicular to it, in certain
positions, and its ready transmission in other positions at right angles
to the former.
Many other substances have the property of polarizing light. If a ray of
light falls upon a transparent medium, which has the same temperature,
density, and structure throughout every part, as fluids, gases, glass,
&c., and a few regularly crystallized minerals, it is refracted into a
single pencil of light by the laws of ordinary refraction, according to
which the ray, passing through the refracting surface from the object to
the eye, never quits a plane perpendicular to that surface. Almost all
other bodies, such as the greater number of crystallized minerals,
animal and vegetable substances, gums, resins, jellies, and all solid
bodies having unequal tensions, whether from unequal temperature or
pressure, possess the property of doubling the image or appearance of an
object seen through them in certain directions; because a ray of natural
light falling upon them is refracted into two pencils which move with
different velocities, and are more or less separated, according to the
nature of the body and the direction of the incident ray. Whenever a ray
of natural light is thus divided into two pencils in its passage through
a substance, both of the transmitted rays are polarized. Iceland spar, a
carbonate of lime, which by its natural cleavage may be split into the
form of a rhombohedron, possesses the property of double refraction in
an eminent degree, as may be seen by pasting a piece of paper, with a
large pin-hole in it, on the side of the spar farthest from the eye. The
hole will appear double when held to the light (N. 205). One of these
pencils is refracted according to the same law as in glass or water,
never quitting the plane perpendicular to the refracting surface, and is
therefore called the ordinary ray. But the other does quit the plane,
being refracted according to a different and much more complicated law,
and on that account is called the extraordinary ray. For the same reason
one image is called the ordinary, and the other the extraordinary image.
When the spar is turned round in the same plane, the extraordinary image
of the hole revolves about the ordinary image, which remains fixed, both
being equally bright. But if the spar be kept in one position, and
viewed through a plate of tourmaline, it will be found that, as the
tourmaline revolves, the images vary in their relative brightness—one
increases in intensity till it arrives at a maximum, at the same time
that the other diminishes till it vanishes, and so on alternately at
each quarter revolution, proving both rays to be polarized. For in one
position the tourmaline transmits the ordinary ray, and reflects the
extraordinary; and, after revolving 90°, the extraordinary ray is
transmitted, and the ordinary ray is reflected. Thus another property of
polarized light is, that it cannot be divided into two equal pencils by
double refraction, in positions of the doubly refracting bodies in which
a ray of common light would be so divided.
Were tourmaline like other doubly refracting bodies, each of the
transmitted rays would be double; but that mineral, when of a certain
thickness, after separating the light into two polarized pencils,
absorbs that which undergoes ordinary refraction, and consequently shows
only one image of an object. On this account tourmaline is peculiarly
fitted for analyzing polarized light, which shows nothing remarkable
till viewed through it or something equivalent.
The pencils of light, on leaving a double refracting substance, are
parallel; and it is clear, from the preceding experiments, that they are
polarized in planes at right angles to each other (N. 206). But that
will be better understood by considering the change produced in common
light by the action of the polarizing body. It has been shown that the
undulations of ether, which produce the sensation of common light, are
performed in every possible plane, at right angles to the direction in
which the ray is moving. But the case is very different after the ray
has passed through a doubly refracting substance, like Iceland spar. The
light then proceeds in two parallel pencils, whose undulations are still
indeed transverse to the direction of the rays, but they are
accomplished in planes at right angles to one another, analogous to two
parallel stretched cords, one of which performs its undulations only in
a horizontal plane, and the other in a vertical or upright plane
(N. 206). Thus the polarizing action of Iceland spar and of all doubly
refracting substances is to separate a ray of common light, whose waves
or undulations are in every plane, into two parallel rays, whose waves
or undulations lie in planes at right angles to each other. By a simple
mechanical law each vibratory motion of the first is resolved into two
vibratory motions at right angles to one another. The ray of common
light may be assimilated to a round rod, whereas the two polarized rays
are like two parallel long flat rulers, one of which is laid
horizontally on its broad surface, and the other horizontally on its
edge. The alternate transmission and obstruction of one of these
flattened beams by the tourmaline is similar to the facility with which
a card may be passed between the bars of a grating or wires of a cage,
if presented edgeways, and the impossibility of its passing in a
transverse direction.
Although it generally happens that a ray of light, in passing through
Iceland spar, is separated into two polarized rays, yet there is one
direction along which it is refracted in one ray only, and that
according to the ordinary law. This direction is called the optic axis
(N. 207). Many crystals and other substances have two optic axes,
inclined to each other, along which a ray of light is transmitted in one
pencil by the law of ordinary refraction. The extraordinary ray is
sometimes refracted towards the optic axis, as in quartz, zircon, ice,
&c., which are therefore said to be positive crystals; but when it is
bent from the optic axis, as in Iceland spar, tourmaline, emerald,
beryl, &c., the crystals are negative, which is the most numerous class.
The ordinary ray moves with uniform velocity within a doubly refracting
substance, but the velocity of the extraordinary ray varies with the
position of the ray relatively to the optic axis, being a maximum when
its motion within the crystal is at right angles to the optic axis, and
a minimum when parallel to it. Between these extremes its velocity
varies according to a determinate law.
It had been inferred, from the action of Iceland spar on light, that in
all doubly refracting substances one only of two rays is turned aside
from the plane of ordinary refraction, while the other follows the
ordinary law; and the great difficulty of observing the phenomena tended
to confirm that opinion. M. Fresnel, however, proved by a most profound
mathematical inquiry, _à priori_, that the extraordinary ray must be
wanting in glass and other uncrystallized substances, and that it must
necessarily exist in carbonate of lime, quartz, and other bodies having
one optic axis, but that in a numerous class of substances, which
possess two optic axes, both rays must undergo extraordinary refraction,
and consequently that both must deviate from their original plane; and
these results have been perfectly confirmed by subsequent experiments.
This theory of refraction, which for generalization is perhaps only
inferior to the law of gravitation, has enrolled the name of Fresnel
among those which pass not away, and makes his early loss a subject of
deep regret to all who take an interest in the higher paths of
scientific research.
When a beam of common light is partly reflected at, and partly
transmitted through a transparent surface, the reflected and refracted
pencils contain equal quantities of polarized light, and their planes of
polarization are at right angles to one another: hence, a pile of panes
of glass will give a polarized beam by refraction. For, if a ray of
common light pass through them, part of it will be polarized by the
first plate, the second plate will polarize a part of what passes
through it, and the rest will do the same in succession, till the whole
beam is polarized, except what is lost by reflection at the different
surfaces, or by absorption. This beam is polarized in a plane at right
angles to the plane of reflection, that is, at right angles to the plane
passing through the incident and reflected ray (N. 208).
By far the most convenient way of polarizing light is by reflection. A
plane of plate-glass laid upon a piece of black cloth, on a table at an
open window, will appear of a uniform brightness from the reflection of
the sky or clouds. But if it be viewed through a plate of tourmaline,
having its axis vertical, instead of being illuminated as before, it
will be obscured by a large cloudy spot, having its centre quite dark,
which will readily be found by elevating or depressing the eye, and will
only be visible when the angle of incidence is 57°, that is, when the
line from the eye to the centre of the black spot makes an angle of 33°
with the surface of the reflector (N. 209). When the tourmaline is
turned round in its own plane, the dark cloud will diminish, and
entirely vanish when the axis of the tourmaline is horizontal, and then
every part of the surface of the glass will be equally illuminated. As
the tourmaline revolves, the cloudy spot will appear and vanish
alternately at every quarter revolution. Thus, when a ray of light is
incident on a pane of plate-glass at an angle of 57°, the reflected ray
is rendered incapable of penetrating a plate of tourmaline whose axis is
in the plane of incidence. Consequently it has acquired the same
character as if it had been polarized by transmission through a plate of
tourmaline, with its axis at right angles to the plane of reflection. It
is found by experience that this polarized ray is incapable of a second
reflection at certain angles and in certain positions of the incident
plane. For if another pane of plate-glass, having one surface blackened,
be so placed as to make an angle of 33° with the reflected ray, the
image of the first pane will be reflected in its surface, and will be
alternately illuminated and obscured at every quarter revolution of the
blackened pane, according as the plane of reflection is parallel or
perpendicular to the plane of polarization. Since this happens by
whatever means the light has been polarized, it evinces another general
property of polarized light, which is, that it is incapable of
reflection in a plane at right angles to the plane of polarization.
All reflecting surfaces are capable of polarizing light, but the angle
of incidence at which it is completely polarized is different in each
substance (N. 210). It appears that the angle for plate-glass is 57°; in
crown-glass it is 56° 55ʹ, and no ray will be completely polarized by
water unless the angle of incidence be 53° 11ʹ. The angles at which
different substances polarize light are determined by a very simple and
elegant law, discovered by Sir David Brewster, “That the tangent of the
polarizing angle for any medium is equal to the sine of the angle of
incidence divided by the sine of the angle of refraction of that
medium.” Whence also the refractive power even of an opaque body is
known when its polarizing angle has been determined.
If a ray, polarized by refraction or by reflection from any substance
not metallic, be viewed through a piece of Iceland spar, each image will
alternately vanish and reappear at every quarter revolution of the spar,
whether it revolves from right to left or from left to right; which
shows that the properties of the polarized ray are symmetrical on each
side of the plane of polarization.
Although there be only one angle in each substance at which light is
completely polarized by one reflection, yet it may be polarized at any
angle of incidence by a sufficient number of reflections. For, if a ray
falls upon the upper surface of a pile of plates of glass at an angle
greater or less than a polarizing angle, a part only of the reflected
ray will be polarized, but a part of what is transmitted will be
polarized by reflection at the surface of the second plate, part at the
third, and so on till the whole is polarized. This is the best
apparatus; but one plate of glass having its inferior surface blackened,
or even a polished table, will answer the purpose.