Circular 
polariza- 
tion. 
(492.) 
Cuar. V., § 3.] 
embraced in Fresnel’s theory, and equally (though 
unknowingly) confirmed by Sir D. Brewster’s labo- 
rious observations. But on one point Fresnel him- 
self obtained a signal triumph. Having deduced ex- 
pressions for the intensity of refracted light, on push- 
ing them to the limit where refraction out of a denser 
into a rarer medium becomes impracticable because 
the light undergoes total internal reflection, the for- 
mule became affected by the multiplier ,/—J, and 
were unsusceptible of arithmetical evaluation. In 
endeavouring to attach a meaning to these expres- 
sions, it occurred to him that as the intensity of the 
totally reflected ray undergoes no change with the 
angle of incidence, the expression in question might 
in some way determine the alteration of the phase of 
the wave (the position and direction of motion of the 
molecules under consideration) which took place at the 
instant of reflection. Now, admitting this as likely, 
it appeared that the phase would vary not only with 
the angle of internal reflection, but with the plane of 
polarization of the ray. It had previously been 
shown by Arago and by himself, that when two oppo- 
sitely polarized rays meet or interfere, though there 
is then no destruction of the light, there is usually 
a remarkable change in its character. There is 
one position of the interfering wave relative to the 
primary one in which the combination produces light 
polarized in a plane exactly intermediate between the 
planes of previous polarization. If either ray be now 
accelerated by half a wave-length on the other, the 
new plane of polarization becomes perpendicular to 
the former ; but if the shift of either of the primary 
rays amounts to only one quarter of a wave-length, 
the motion of the molecules takes place in a circle, 
and the undulation has a helical form. Now, Fresnel 
tested his hypothesis concerning totally reflected light 
by calculating the circumstances of incidence which 
should produce an effect equivalent to this; and the 
result completely verified his bold conjecture. The 
apparatus employed is called Fresnel’s Rhomb, which 
transforms plane-polarized light into light equally 
reflexible in all azimuths, yet not common light, be- 
cause it possesses properties which common light does 
not (such as displaying the rings in crystals); this 
is termed circularly polarized light. 
Theory of Double Refraction—The difficulty of 
Double re- accounting for double refraction did not consist 
on exX- 
plained. 
in showing how a spheroidal wave might be pro- 
pagated. Young had already shown, in 1809, that 
it would result from supposing a lamellar arrange- 
ment of the crystalline molecules so that the ether 
was differently elastic in a direction parallel to the 
axis than in a plane or planes perpendicular to 
that line. Huygens had shown something similar 
in accounting for terrestrial atmospheric refraction. 
The difficulty was, to account for two waves travel- 
OPTICS.—FRESNEL. 
905 
ling at the same time through the same portion of 
matter with unequal velocities. The moment that 
the idea of molecular movement transverse to the line 
of propagation was admitted, it was easy to see that 
no contradiction was involved in the idea. Two 
waves might simultaneously travel in the same direc- 
tion, and through the same medium, provided the 
molecular displacements were in different planes. So 
happy a solution could hardly fail to strike such minds 
as those of Young and Fresnel with the impress of 
conviction. A closer analysis confirmed the proba- 
bility. Iceland spar (or rather the ether imprisoned. 
within it) is conceived of as a medium of uniform elas- 
ticity in all planes perpendicular to the axis, but of a 
different and greater elasticityin any direction parallel 
to the axis. It is shown to result from this, that in 
the direction of the axis alone is the motion of light 
independent of the plane of the vibrations of which it 
is composed, and consequently no separation of rays 
occurs. When a ray moves parallel to what may by 
an analogy be called the equatoreal plane of the 
erystal, its undulation will, generally speaking, be 
resolved into two whose vibrations are parallel and 
perpendicular to that plane, and which travel with 
different velocities though in the same direction. If 
the ray take any other direction through the crystal, 
both the direction and velocity of the divided rays 
differ, The form of the extraordinary wave is exactly 
the spheroid of Huygens. 
But what are we to conclude concerning those crys- 
tals (of the discovery of which we shall speak in § faa ae 
Wises ; ith t 
once assumed that the elasticities must in that case axes, a 
presenting two axes of double refraction? Fresnel at 
vary in three rectangular directions, and he proceeded 
to caleulate the manner of propagation of a wave 
through a medium thus constituted, I had proposed 
to attempt some explanation of the steps of his most 
ingenious and profound argument, but I find it incom- 
patible with the space at my disposal, and at any 
rate hardly to be apprehended without the use of 
symbols or figures. For these reasons I shall merely 
state the results. When the medium presents un- 
equal elasticities in three rectangular directions, the 
surface of the wave consists of two sheets each tra- 
velling with its peculiar velocity. But neither of 
these being spherical, the result cannot be expressed 
by the ordinary law of refraction. In two directions 
within the crystal, the wave surfaces coincide, or the 
two rays coalesce. These directions are evidently 
the optic axes, and the wave surface in their neigh- 
bourhood has very interesting geometrical and 
physical properties which have been elucidated 
by British philosophers, as will be noticed in 
another section. The true optical axes cannot 
exceed two, and when two of the three elasticities 
become equal, they merge into one. This is the 
1 Young’s reasoning (Quarterly Review 1809, and Works, vol. i. p. 228) is based on an experiment by Chladni on the differing 
velocity with which sound is propagated in wood, depending on the direction of the fibres. 
VoL. T 
by 
