DISCOVERY OF THE LAWS OF PHENOMENA OF DIPOLARIZED LIGHT.
BESIDES the above-mentioned perplexing cases of colors produced by
common light, cases of _periodical colors produced by polarized
light_ began to be discovered, and soon became numerous. In August,
1811, M. Arago communicated to the Institute of France an account of
colors seen by passing polarized light through mica, and
_analysing_[57\9] it with a prism of Iceland spar. It is remarkable
that the light which produced the colors in this case was the light
polarized by the sky, a cause of polarization not previously known.
The effect which the mica thus produced was termed
_depolarization_;--not a very happy term, since the effect is not
the destruction of the polarization, but the combination of a new
polarizing influence with the former. The word _dipolarization_,
which has since been proposed, is a much more appropriate
expression. Several other curious phenomena of the same kind were
observed in quartz, and in flint-glass. M. Arago was not able to
reduce these phenomena to laws, but he had a full conviction of
their value, and ventures to class them with the great steps in {81}
this part of optics. "To Bartholin we owe the knowledge of double
refraction; to Huyghens, that of the accompanying polarization; to
Malus, polarization by reflection; to Arago, depolarization." Sir D.
Brewster was at the same time engaged in a similar train of
research; and made discoveries of the same nature, which, though not
published till some time after those of Arago, were obtained without
a knowledge of what had been done by him. Sir D. Brewster's
_Treatise on New Philosophical Instruments_, published in 1813,
contains many curious experiments on the "depolarizing" properties
of minerals. Both these observers noticed the changes of color which
are produced by changes in the position of the ray, and the
alternations of color in the two oppositely polarized images; and
Sir D. Brewster discovered that, in topaz, the phenomena had a
certain reference to lines which he called the _neutral_ and
_depolarizing_ axes. M. Biot had endeavored to reduce the phenomena
to a law; and had succeeded so far, that he found that in the plates
of sulphate of lime, the place of the tint, estimated in Newton's
_scale_ (see _ante_, chap. vii.), was as the square of the sine of
the inclination. But the laws of these phenomena became much more
obvious when they were observed by Sir D. Brewster with a larger
field of view.[58\9] He found that the colors of topaz, under the
circumstances now described, exhibited themselves in the form of
elliptical rings, crossed by a black bar, "the most brilliant class
of phenomena," as he justly says, "in the whole range of optics." In
1814, also, Wollaston observed the circular rings with a black
cross, produced by similar means in calc-spar; and M. Biot, in 1815,
made the same observation. The rings in several of these cases were
carefully measured by M. Biot and Sir D. Brewster, and a great mass
of similar phenomena was discovered. These were added to by various
persons, as M. Seebeck, and Sir John Herschel.
[Note 57\9: The prism of Iceland spar produces the colors by
separating the transmitted rays according to the laws of double
refraction. Hence it is said to _analyse_ the light.]
[Note 58\9: _Phil. Trans._ 1814.]
Sir D. Brewster, in 1818, discovered a general relation between the
crystalline form and the optical properties, which gave an
incalculable impulse and a new clearness to these researches. He
found that there was a correspondence between the degree of symmetry
of the optical phenomena and the crystalline form; those crystals
which are uniaxal in the crystallographical sense, are also uniaxal
in their optical properties, and give circular rings; those which
are of other forms are, generally speaking, biaxal; they give oval
and knotted _isochromatic_ lines, with two _poles_. He also
discovered a rule for the tint at each point {82} in such cases; and
thus explained, so far as an empirical law of phenomena went, the
curious and various forms of the colored curves. This law, when
simplified by M. Biot,[59\9] made the tint proportional to the
product of the distances of the point from the two poles. In the
following year, Sir J. Herschel confirmed this law by showing, from
actual measurement, that the curve of the isochromatic lines in
these cases was the curve termed the _lemniscata_, which has, for
each point, the product of the distances from two fixed poles equal
to a constant quantity.[60\9] He also reduced to rule some other
apparent anomalies in phenomena of the same class.
[Note 59\9: _Mém. Inst._ 1818, p. 192.]
[Note 60\9: _Phil. Trans._ 1819.]
M. Biot, too, gave a rule for the directions of the planes of
polarization of the two rays produced by double refraction in biaxal
crystals, a circumstance which has a close bearing upon the
phenomena of dipolarization. His rule was, that the one plane of
polarization bisects the dihedral angle formed by the two planes
which pass through the optic axes, and that the other is
perpendicular to such a plane. When, however, Fresnel had discovered
from the theory the true laws of double refraction, it appeared that
the above rule is inaccurate, although in a degree which observation
could hardly detect without the aid of theory.[61\9]
[Note 61\9: Fresnel, _Mém. Inst._ 1827, p. 162.]
There were still other classes of optical phenomena which attracted
notice; especially those which are exhibited by plates of quartz cut
perpendicular to the axis. M. Arago had observed, in 1811, that this
substance produced a _twist_ of the plane of polarization to the right
or left hand, the amount of this twist being different for different
colors; a result which was afterwards traced to a modification of
light different both from common and from polarized light, and
subsequently known as _circular polarization_. Sir J. Herschel had
the good fortune and sagacity to discover that this peculiar kind of
polarization in quartz was connected with an equally peculiar
modification of crystallization, the _plagihedral_ faces which are
seen, on some crystals, obliquely disposed, and, as it were,
following each other round the crystal from left to right, or from
right to left. Sir J. Herschel found that the _right-handed_ or
_left-handed_ character of the circular polarization corresponded,
in all cases, to that of the crystal.
In 1815, M. Biot, in his researches on the subject of circular
polarization, was led to the unexpected and curious discovery, that
this {83} property which seemed to require for its very conception a
crystalline structure in the body, belonged nevertheless to several
fluids, and in different directions for different fluids. Oil of
turpentine, and an essential oil of laurel, gave the plane of
polarization a rotation to the left hand; oil of citron, syrup of
sugar, and a solution of camphor, gave a rotation to the right hand.
Soon after, the like discovery was made independently by Dr.
Seebeck, of Berlin.
It will easily be supposed that all those brilliant phenomena could
not be observed, and the laws of many of the phenomena discovered,
without attempts on the part of philosophers to combine them all
under the dominion of some wide and profound theory. Endeavors to
ascend from such knowledge as we have spoken of, to the general
theory of light, were, in fact, made at every stage of the subject,
and with a success which at last won almost all suffrages. We are
now arrived at the point at which we are called upon to trace the
history of this theory; to pass from the laws of phenomena to their
causes;--from Formal to Physical Optics. The undulatory theory of
light, the only discovery which can stand by the side of the theory
of universal gravitation, as a doctrine belonging to the same order,
for its generality, its fertility, and its certainty, may properly
be treated of with that ceremony which we have hitherto bestowed
only on the great advances of astronomy; and I shall therefore now
proceed to speak of the Prelude to this epoch, the Epoch itself, and
its Sequel, according to the form of the preceding Book which treats
of astronomy.
[2nd Ed.] [I ought to have stated, in the beginning of this chapter,
that Malus discovered the depolarization of _white light_ in 1811.
He found that a pencil of light which, being polarized, refused to
be reflected by a surface properly placed, recovered its power of
being reflected after being transmitted through certain crystals and
other transparent bodies. Malus intended to pursue this subject,
when his researches were terminated by his death, Feb. 7, 1812. M.
Arago, about the same time, announced his important discovery of the
depolarization of _colors_ by crystals.
I may add, to what is above said of M. Biot's discoveries respecting
the circular polarizing power of fluids, that he pursued his
researches so as to bring into view some most curious relations
among the elements of bodies. It appeared that certain substances,
as sugar of canes, had a right-handed effect, and certain other
substances, as gum, a left-handed effect; and that the molecular
value of this effect was not altered by dilution. It appeared also
that a certain element of the {84} substance of fruits, which had
been supposed to be gum, and which is changed into sugar by the
operation of acids, is not gum, and has a very energetic
right-handed effect. This substance M. Biot called _dextrine_, and
he has since traced its effects into many highly curious and
important results.**]
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PHYSICAL OPTICS.