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The degree of compression to whicli the glass is to be subjected, to produce these effects, is such that when the compressed glass is placed in the polariscope, with the tourmalines crossed, a black cross is seen with blond-white vacant spaces in the corners. Unannealed glass, possessing the same degree of doubly refracting power, acts in a similar manne'r to compressed glass.
Annealed glass,while either rapidly heating or cooling, likewise
gives rise to similar effects at the time when its doubly refracting
power is just equal to that of the compressed glass above described.
4. Quartz. — I now proceed to notice the remarkable optical
properties of the substance denominated Quartz.
This term, the etymological origin of which is not clearly made out, is applied to some of the crystalline forms of silica. The transparent variety, called rock or mountain crystal, is the kind used for optical purposes. Very perfect transparent crystals are found near Bristol and in Cornwall, and are called Bristol or Cornish diamonds. The opticians cut some of the most limpid and large crystals, which usually come from the Brazils, for making lenses for spectacles and eye-glasses, and which they denominate pebbles.
Quartz belongs to the rhombohedric system. Its most common form is the six-sided prism, terminated by six-sided pyramids (fig.48). Its fracture is conchoidal.
Now, as quartz belongs to the same system of crystals to which Iceland spar belongs, it might be expected that when we place a plate of it, cut perpendicularly to its principal or prismatic axis (fig. 49 o a), in the polariscope, we should observe the cross and a system of circular rings, as in the case of Iceland spar and other crystals of the rhombohedric system. But this is not the case. We do, indeed, observe a system of rings, but the centre of the cross is wanting (fig. 50). Instead of the cross within the inner ring we observe an uniform tint, the colour of which changes when the analyzer is revolved; and, in succession, Different modes of silt- all the colours of the spectrum are brought purposes" °r optical into view. But the order of succession (supaa. Plates transverse posing the direction or revolution of the ana
to the prismatic axis, for F B . . .....-,
showing (in the poiari- lyzer to remain the same) varies in different
cX)ri*ng!sXte5TM?fCir' c.rysta,s- Thus. suppose we turn the analyzer bb. Plates cut obliquely right-handed, that is, as we screw up, the
tnetsl^ht,bandsh0win! colours succeed each other, either in this cc. wedges for making order — red, oranqe, yellow, qreen, blue, in
Wollaston's quartz dou- .. '».»• j • .1
biy refracting prisms. digo, violet, red again, and so on; or in the
Ordinary Vryttal of
In each of these diagrams the arrow shows the direction in which the analyzer is to be rotated, in order to obtain the spectral tints in the descending order. In one complete revolution of the analyzer each of the colours of the spectrum occurs twice. In other words, all the colours are seen in one semi-revolution of the analyzer.
Hence those specimens of quartz which present the colours in the descending order by a right-handed rotation of the analvzer, are denominated dextrogyrate, or right-handed quartz; while those which present them by a left-handed rotation are called 1<bvogyrate, or left-handed quartz.
Fio. 63. Between these two varieties there has been
discovered by Sir John Herschel another dif
/sk ference. In that form of quartz, termed by
// ^.\ Haiiy plagiedral (from irXdytos oblique, and
cSpa a base), it has been found that when the
unsymmetrical or plagiedral faces (fig. 53 x)
U /;:;: lean to the right, the polarization is right
v\// handed, and vice versa', when they lean to the
left the polarization is left-handed. So that the
Plagiedral Quartz, cause, whatever it may be, which determines
the optical phenomena is also connected with the production of
the plagiedral faces.
If, instead of using white light in our experiments, we employ homogeneous light, we find that the plane of polarization of the incident rays is turned or made to rotate either to the right or left, according as the quartz plate is either right-handed or lefthanded. This rotation of the plane of polarization of the incident ray is proportional to the thickness of the plate. The rings produced by thin plates are broader and less numerous than those produced by thick plates. If two plates be superposed the effect is, very nearly, the same as that produced by a single plate whose thickness is either the sum or the difference of the thicknesses of the two plates; according as they are of the same kind (that is, both either right-handed or left-handed), or of opposite kinds (that is, one right-handed, the other left-handed). Thus, if the rotation of the red rays, effected by a plate of quartz of -jijth of an inch thick be equal to 17J°, that produced by two superposed plates of equal thickness, taken from the same crystal, will be 2x 17J°=35°. On the other hand, if we combine a plate of right-handed quartz of -^th of an inch thick with a plate of left-handed quartz of -/j-ths of an inch thick, the same effects are produced as if we had employed a left-handed plate of-^-ths of an inch thick. When the thicknesses of the two dissimilar plates are equal " the plates of course destroy each other's effects, and the system of rings with the black cross will be distinctly seen." (Brewster).
The rotation of the plane of polarization increases with the refrangibility of the rays. Thus it is greater with violet than with blue, with blue than yellow, and with yellow than red.
Homogeneous Ray. Arc of Rotation.
Extreme Bed 17°29'47"
Limit of Bed and Orange 20° 28' 47"
"Orange and Yellow 22° 18'49"
«* Yellow and Green 25° 40'31"
"Green and Blue 30° 2'45"
"Blue and Indigo 34° 34' 18"
"Indigo and Violet 37° 51' 58"
"Extreme Violet 44° 4' 58"
I come now to the explanation which the wave hypothesis offers of these phenomena.
When the light, rectilinearly polarized by the first tourmaline plate, is incident on the quartz plate, it suffers double refraction. To prove this, Fresnel contrived a combination of a right-handed prism, and two halves of a left-handed one, by which he doubled the separation of the two rays, and in this way managed to demonstrate the actual existence of double refraction in the principal or prismatic axis of quartz. This is a most remarkable fact. In the principal or prismatic axis of every other known crystal of the rhombohedric system double refraction does not exist.
But the two rays thus obtained differ in their properties from those produced by Iceland spar and other doubly refracting crystals, for while the latter are rectilinearly polarized, those of quartz are circularly polarized. Now every circularly polarized ray is equal to two rectilinearly polarized waves, differing in their progress an odd number of J undulations. It follows therefore, that the two circularly polarized waves are equal to four rectilinearly polarized waves. Hence then to explain the phenomena, we must assume that the rectilinearly polarized ray (which I shall call R) incident on the quartz, is resolved into two others (.A and B) of equal intensity, the one (A) polarized in a plane 45° inclined to the right, the other (2?) 45° inclined to the left of the plane of polarization of the primitive ray (R). Let us further conceive that each of the two rays (A and B) is resolved into two other rays, namely A into Aa and Ab, and B into Ba and Bb. Aa and Ab are polarized in one plane, viz., + 45°, while Ba and Bb are polarized in another plane, viz.,—45". Aa and Ba have each their phases advanced, or + ^ undulation, while Ab and Bb have each their phases retarded, or —-J- undulation *. Now if we suppose these four rays to be combined two and two in a cross order, we shall have resulting two circularly polarized rays, one right-handed, the other left-handed. Thus Aa and Bb combine to form a left-handed ray, while Ab and Ba form a right-handed one. For when the advanced system of waves has its plane of polarization to the right of that of the retarded system, the ethereal molecules rotate from right to left; whereas they rotate from left to right when the first plane is to the left of the second.
These two circularly polarized rays are propagated along the axis of quartz with unequal velocities. In right-handed quartz, the right-handed ray is transmitted with greater velocity, in lefthanded quartz with lesser velocity than the left-handed ray ; and thus at their emergence one is in advance of the other. If the surface of egress or ingress be oblique to the axis, the two circularly polarized rays will emerge in different directions; but if it be perpendicular (as in the experiment under examination) they will emerge superposed, and will compound a single ray polarized
* "It results from the laws of interference," says Fresnel, " that a system of waves, polarized rectilinearly, may be replaced by two others, polarized at right angles to each other, and coinciding in their route ; and that for each of these we may substitute two other systems of waves having the same plane of polarization, but the one advanced, the other retarded Jth of an undulation; and thus separated Jth of an undulation. In this way are obtained four systems of waves of equal intensity, of which two, polarized at right angles to each other, are Jth of an undulation behind the two others polarized in the same planes."
in a single plane. Now this plane is removed from the plane of primitive polarization by an angle proportional to the interval of retardation (therefore, proportional to the thickness of the crystal) and to the refrangibility of the ray.
Thus then the differently coloured rays emerge from the quartz plate polarized in different planes; hence, by rotating the analyzer, they are successively transmitted and brought into view.
The following diagram may, perhaps, serve to render more intelligible the explanations of the action of a plate of quartz, of one millimetre (0.03937 of an English inch) in thickness, on the incident reclilinearly polarized red light.
A succession of quartz prisms does not give a further multiplication of images—a circumstance which distinguishes the double refraction of quartz from that of Iceland spar and other crystals.
The above explanation is applicable only when the direction of the rays coincides with the principal axis of the crystal. When it is inclined to this axis, Mr. Airy has shown that the two resulting rays are elliptically polarized, the elliptical vibrations in the two rays being in opposite directions (that is, one righthanded, the other left-handed), and the greater axis of the ellipse is for the extraordinary ray, in the principal plane of the crystal, and, for the ordinary ray, in a plane perpendicular to the principal one. The ratio of the axes in these ellipses, varies with the inclination of the ray to the principal axis of the crystal. When the direction of the ray coincides with this axis, the ratio is one of equality, and the ellipses become circles. But when the ray is inclined to the axis, the ratio increases indefinitely with the inclination. "It is also necessary to suppose that the axis of revolution of the spheroid (prolate for quartz) in which the extraordinary ray is supposed to diverge, is less than the radius of the sphere into which the ordinary wave diverges."
Hitherto we have had no satisfactory theory of the cause of the unequal velocities with which the two rays are transmitted along the principal axis of quartz. We conceive that it must depend either on some peculiarity in the molecules themselves,