DISCOVERY OF THE LAWS OF POLARIZATION.
IF the Extraordinary Refraction of Iceland spar had appeared
strange, another phenomenon was soon noticed in the same {73}
substance, which appeared stranger still, and which in the sequel
was found to be no less important. I speak of the facts which were
afterwards described under the term _Polarization_. Huyghens was the
discoverer of this class of facts. At the end of the treatise which
we have already quoted, he says,[42\9] "Before I quit the subject of
this crystal, I will add one other marvellous phenomenon, which I
have discovered since writing the above; for though hitherto I have
not been able to find out its cause, I will not, on that account,
omit pointing it out, that I may give occasion to others to examine
it." He then states the phenomena; which are, that when two
rhombohedrons of Iceland spar are in parallel positions, a ray
doubly refracted by the first, is not further divided when it falls
on the second: the ordinarily refracted ray is ordinarily refracted
_only_, and the extraordinary ray is only extraordinarily refracted
by the second crystal, neither ray being doubly refracted. The same
is still the case, if the two crystals have their _principal planes_
parallel, though they themselves are not parallel. But if the
principal plane of the second crystal be perpendicular to that of
the first, the reverse of what has been described takes place; the
ordinarily refracted ray of the first crystal suffers, at the
second, extraordinary refraction _only_, and the extraordinary ray
of the first suffers ordinary refraction only at the second. Thus,
in each of these positions, the double refraction of each ray at the
second crystal is reduced to single refraction, though in a
different manner in the two cases. But in any other position of the
crystals, each ray, produced by the first, is doubly refracted by
the second, so as to produce four rays.
[Note 42\9: _Tr. Opt._ p. 252.]
A step in the right conception of these phenomena was made by
Newton, in the second edition of his _Opticks_ (1717). He
represented them as resulting from this;--that the rays of light
have "sides," and that they undergo the ordinary or extraordinary
refraction, according as these sides are parallel to the principal
plane of the crystal, or at right angles to it (Query 26). In this
way, it is clear, that those rays which, in the first crystal, had
been selected for extraordinary refraction, because their sides were
perpendicular to the principal plane, would all suffer extraordinary
refraction at the second crystal for the same reason, if its
principal plane were parallel to that of the first; and would all
suffer ordinary refraction, if the principal plane of the second
crystal were perpendicular to that of the first, and {74}
consequently parallel to the sides of the refracted ray. This view
of the subject includes some of the leading features of the case,
but still leaves several considerable difficulties.
No material advance was made in the subject till it was taken up by
Malus,[43\9] along with the other circumstances of double refraction,
about a hundred years afterwards. He verified what had been observed
by Huyghens and Newton, on the subject of the variations which light
thus exhibits; but he discovered that this modification, in virtue of
which light undergoes the ordinary, or the extraordinary, refraction,
according to the position of the plane of the crystal, may be
impressed upon it many other ways. One part of this discovery was made
accidentally.[44\9] In 1808, Malus happened to be observing the light
of the setting sun, reflected from the windows of the Luxembourg,
through a rhombohedron of Iceland spar; and he observed that in
turning round the crystal, the two images varied in their intensity.
Neither of the images completely vanished, because the light from the
windows was not properly modified, or, to use the term which Malus
soon adopted, was not completely _polarized_. The complete
polarization of light by reflection from glass, or any other
transparent substance, was found to take place at a certain definite
angle, different for each substance. It was found also that in all
crystals in which double refraction occurred, the separation of the
refracted rays was accompanied by polarization; the two rays, the
ordinary and the extraordinary, being always polarized _oppositely_,
that is, in planes at right angles to each other. The term _poles_,
used by Malus, conveyed nearly the same notion as the term _sides_
which had been employed by Newton, with the additional conception of a
property which appeared or disappeared according as the _poles_ of the
particles were or were not in a certain direction; a property thus
resembling the _polarity_ of magnetic bodies. When a spot of polarized
light is looked at through a transparent crystal of Iceland spar, each
of the two images produced by the double refraction varies in
brightness as the crystal is turned round. If, for the sake of
example, we suppose the crystal to be turned round in the direction of
the points of the compass, N, E, S, W, and if one image be brightest
when the crystal marks N and S, it will disappear when the crystal
marks E and W: and on the contrary, the second image will vanish when
the crystal marks N and S, {75} and will be brightest when the crystal
marks E and W. The first of these images is polarized _in the plane_
NS passing through the ray, and the second _in the plane_ EW,
perpendicular to the other. And these rays are _oppositely_ polarized.
It was further found that whether the ray were polarized by reflection
from glass, or from water, or by double refraction, the modification
of light so produced, or the nature of the polarization, was identical
in all these cases;--that the alternatives of ordinary and
extraordinary refraction and non-refraction, were the same, by
whatever crystal they were tested, or in whatever manner the
polarization had been impressed upon the light; in short, that the
property, when once acquired, was independent of everything except the
sides or _poles_ of the ray; and thus, in 1811, the term
"polarization" was introduced.[45\9]
[Note 43\9: Malus, _Th. de la Doub. Réf._ p. 296.]
[Note 44\9: Arago, art. _Polarization_, Supp. _Enc. Brit._]
[Note 45\9: _Mém. Inst._ 1810.]
This being the state of the subject, it became an obvious question,
by what other means, and according to what laws, this property was
communicated. It was found that some crystals, instead of giving, by
double refraction, two images oppositely polarized, give a single
polarized image. This property was discovered in the agate by Sir D.
Brewster, and in tourmaline by M. Biot and Dr. Seebeck. The latter
mineral became, in consequence, a very convenient part of the
apparatus used in such observations. Various peculiarities bearing
upon this subject, were detected by different experimenters. It was
in a short time discovered, that light might be polarized by
refraction, as well as by reflection, at the surface of
uncrystallized bodies, as glass; the plane of polarization being
perpendicular to the plane of refraction; further, that when a
portion of a ray of light was polarized by reflection, a
corresponding portion was polarized by transmission, the planes of
the two polarizations being at right angles to each other. It was
found also that the polarization which was incomplete with a single
plate, either by reflection or refraction, might be made more and
more complete by increasing the number of plates.
Among an accumulation of phenomena like this, it is our business to
inquire what general laws were discovered. To make such discoveries
without possessing the general theory of the facts, required no
ordinary sagacity and good fortune. Yet several laws were detected
at this stage of the subject. Malus, in 1811, obtained the important
generalization that, whenever we obtain, by any means, a polarized
ray of light, we produce also another ray, polarized in a contrary
{76} direction; thus when reflection gives a polarized ray, the
companion-ray is refracted polarized oppositely, along with a
quantity of unpolarized light. And we must particularly notice _Sir
D. Brewster's rule_ for the _polarizing angle_ of different bodies.
Malus[46\9] had said that the angle of reflection from transparent
bodies which most completely polarizes the reflected ray, does not
follow any discoverable rule with regard to the order of refractive
or dispersive powers of the substances. Yet the rule was in reality
very simple. In 1815, Sir D. Brewster stated[47\9] as the law, which
in all cases determines this angle, that "the index of refraction is
the tangent of the angle of polarization." It follows from this,
that the polarization takes place when the reflected and refracted
rays are at right angles to each other. This simple and elegant rule
has been fully confirmed by all subsequent observations, as by those
of MM. Biot and Seebeck; and must be considered one of the happiest
and most important discoveries of the laws of phenomena in Optics.
[Note 46\9: _Mém. Inst._ 1810.]
[Note 47\9: _Phil. Trans._ 1815.]
The rule for polarization by one reflection being thus discovered,
tentative formulæ were proposed by Sir D. Brewster and M. Biot, for
the cases in which several reflections or refractions take place.
Fresnel also in 1817 and 1818, traced the effect of reflection in
modifying the direction of polarization, which Malus had done
inaccurately in 1810. But the complexity of the subject made all
such attempts extremely precarious, till the theory of the phenomena
was understood, a period which now comes under notice. The laws
which we have spoken of were important materials for the
establishment of the theory; but in the mean time, its progress at
first had been more forwarded by some other classes of facts, of a
different kind, and of a longer standing notoriety, to which we must
now turn our attention.