244

COLOURED RINGS OF POLARIZED LIGHT.

[125.

colours which are observed. The formation of the cross is occasioned by the absence of any change in the plane of polarization of those rays which traverse the principal section of the crystal which either coincides with the plane of polarization, or is perpendicular to it; these rays, consequently, do not interfere when analysed by the tourmaline. The arms of the cross are alternately white or black according as the axis of the tourmaline is parallel to the original plane of polarization, or is at right angles to it.

With biaxal crystals, such as aragonite, plumbic carbonate, nitre, and borax, the phenomena are even more beautiful, a double system of rings being formed, in which the curves are of a different order, owing to the more complicated phenomena resulting from the mutual action of the optic axes; the surface of the section being oblique to both these axes: the greater the angle formed with each other by the axes, the further will the rings be asunder. The two axes are inclined to each other in nitre at an angle of 5° 20′; in aragonite at an angle of 18° 18': in borax at an angle of 28° 42'; and in topaz the angle is between 49° and 50°: the position of the intersecting cross varies when the crystalline plate is made to rotate; and the colours become complementary when the analyser is turned round. The general outline of these figures is represented in fig. 106.

In a plate of quartz cut perpendicularly to the axis the rings are also beautifully shown when examined in the same way; the centre is however brightly coloured, and the crosses only seen at some distance from the centre. When a plate of the same material, but cut parallel to the axis, is examined by monochromatic light, a series of hyperbolic curves is observed, and if the surfaces of the plate make an angle of 45° with the axis of the crystal, the curves are projected as straight lines. With white light the curves are not perceived in consequence of the mixing of the different colours. Two such plates crossed and examined in the polariscope show straight lines even with white light, the centre line being black and the others coloured when the polarizer and analyser are crossed: when they are parallel a

125.]

COLOURED RINGS OF POLARIZED LIGHT.

245

white line is seen in the centre with one dark line at each side and coloured ones beyond. When the planes of vibration of polarizer and analyser are inclined at an angle of 45° the lines disappear. If the vibration planes of the quartz are parallel and perpendicular to that of the polarizer, no lines are seen with any position of the analyser. A combination of two such plates and a plate of tourmaline constitutes Savart's polariscope, an instrument capable of detecting the slightest traces of polarized light. Two plates of Iceland spar or of selenite of suitable thickness exhibit the same phenomenon.

An interesting connexion has been established between the phenomena of coloured lines and rings and the state of molecular elasticity in the solid, by the discovery that these appearances may at will be produced in uncrystallized media, such as glass, or in regular crystals, whenever homogeneity is interfered with in regular progression. This fact is rendered evident by the application of pressure, laterally, to a strip of glass which previously exerted no doubly refracting influence. The parts compressed acquire a negative double refraction; and they are separated, by a neutral line where the particles of the solid retain their normal condition, from those on the opposite edge, which have become dilated, and show positive double refraction. This want of homogeneity exists permanently in glass which has been imperfectly annealed; and, according to the form given to it by grinding, it is possible to alter the elasticity of the particles in different directions, and produce the phenomena of uniaxal or of biaxal crystals; a square or a circular plate, for instance, belongs to the uniaxal

system (as shown in fig. 107), while an elliptic plate occasions rings referable to the biaxal form. This fact suggests the probability of the existence of a molecular stress in doubly refracting crystals, and consequently direc

FIG. 107.

田4

tions in the crystal in which the elasticity of the ether particles differ. The greater the elasticity in a direction parallel to the plane of vibration of the ether particles the more rapid will be the transmission of the ray of light. In bodies exhibiting simple refraction the elasticity is uniform in all directions; in uniaxal positive crystals the axis of minimum elasticity coincides with the optic

246

COLOURED ROTATORY POLARIZATION.

[125

axis, in negative crystals the axis of maximum elasticity lies in this direction. Biaxal crystals exhibit three axes of unequal elasticity.

(126) Coloured Rotatory (Circular) Polarization.-There are, however, cases in which the plane of polarization of the ray is continually changing, during its entire progress through the medium employed to produce the colouration; in some substances the plane of polarization revolves from left to right (like the hands of a clock facing the observer); in others from right to left. Rock crystal was the substance in which this effect was first observed. If a polarized ray be transmitted through a plate of rock crystal cut in a direction perpendicular to that of the axis of the prism, the plane of polarization undergoes rotation in a degree proportioned to the thickness of the plate. The amount of this rotation differs for each colour, and increases according to the increase of the refrangibility of the ray. If the incident light be white, the emerging light, when examined by an analysing plate, is therefore seen to be coloured. The central portion only of the pencil of light (which traverses the plate normally, parallel to its optic axis) exhibits these phenomena; at oblique incidences, the usual law of interference prevails, and coloured rings are formed. Certain crystals of quartz produce left-handed, certain other crystals of it, righthanded polarization. In right-handed quartz the central colours ascend in the scale, when the analyser is turned in the direction of the hands of a watch, the succession being red, orange, yellow, green, &c., and the rings appear to expand with the revolution of the analyser. When homogeneous light is employed, each colour disappears at a particular angle of the analyser. In crystals of quartz of a different hemihedral form, or in which the secondary planes of the crystal are arranged differently from those of the right-handed variety, the same phenomena occur, but in the opposite direction. Sodic chlorate, which crystallizes in forms belonging to the regular system, yields hemihedral crystals, and exhibits a power of rotation over the polarized ray, analogous to that of quartz; the rotation being right-handed or lefthanded, according as the crystal is hemihedral to the right or to the left. The terms right- and left-handed rotation refer to the direction in which the plane of polarization has been turned when the observer is facing the instrument with the beam of light passing towards him. Thus, suppose a beam of monochromatic light from a spirit lamp containing a small quantity of sodic chloride to be passing into the polariscope, the analyser

126.]

COLOURED ROTATORY POLARIZATION.

247

being so placed that the light is not transmitted; if now a piece of right-handed quartz be placed between the polarizer and analyser, the light will be transmitted, and in order to render it again invisible the analyser must be turned to the right, that is, in the direction of the hands of a watch facing the observer. If we consider the change with reference to a polarized ray passing from its source through a piece of right-handed quartz, it is clear that the plane of polarization is rotated to the left. When white light is passed into the polariscope in which a plate of right-handed quartz 3 or 4" 4mm. in thickness is placed and the light transmitted by the analyser examined by a spectroscope, a dark band will be observed crossing the spectrum. If the analyser be now rotated to the right, the black band will travel along the spectrum from the red towards the violet end. The colour, therefore, which is seen when the eye is applied direct to the analyser consists of a mixture of the colours of the spectrum complementary to that represented by the black band. The passage of the band from the red to the orange, yellow, green, blue, and violet, corresponds to the change of the complementary green to blue, violet, red, orange, and yellow, although it is perhaps inappropriate to apply these names to the different tints which are so complex in their nature.

When a plane polarized ray enters a plate of rock crystal cut perpendicularly to the axis, the ray is decomposed into two, but the conditions of the rays are essentially different from those produced when a polarized ray is transmitted into a plate of selenite; whereas in the latter the motions of the ether particles consist of straight lines lying in a plane so that each component ray is plane polarized, in quartz the ether particles move in circles. In one of the component waves the ether particles move in one direction and in the other ray in the opposite; the velocity of rotation of the particles is the same in both rays, but one of them proceeds more rapidly through the crystal than the other. The effect of circular vibrations of this kind is to produce rays of light traversing the crystal in the form of a helix, those particles which move in a right-handed direction producing a left-handed helix. This may be roughly illustrated by placing on a table a vertical cylinder and hanging by it a chain. of beads rather longer than the cylinder. If one end of the chain be held in the hand and slowly rotated round the upper edge of the cylinder while the other end rests on the table, each bead will be seen to move round the cylinder in a circular path, while the string of beads will show a helical line: if the rotation

248

COLOURED ROTATORY POLARIZATION.

[126.

is right-handed (or in the direction of the hands of a clock) the helix will be seen to be left-handed. Let fig. 107 a represent a

G

E

FIG. 107 a.

AB

plate of quartz of which the axis is shown by the arrow A B, and let us suppose that plane polarized light is passing upwards through the plate, the plane of vibration being shown by the double headed arrow on the base c D, the ether particles on the circle c D will K move in opposite directions, those rotating in the direction e » will originate the helical ray e m n o p q r, and those moving in the direction e c will originate the ray es tu v. It will be seen that the former of these makes one and a half turns round the cylinder, while the latter makes only one turn; the former therefore traverses the crystal more slowly than the latter. Let us

now consider the action of these circularly rotating ether particles at the moment of emerging of the helical rays from the crystal on an ether particle y

in the medium above the crystal. The particle at r at a certain moment is moving in the direction r w, and at the same instant that atv will be moving in the direction vw: the result of these two motions will be the movement of y towards w; it will be readily seen that the effect of the motions of two particles from æ to w, one describing the path a v w and the other a r w, will be to move a particle from a to w so as to originate a plane wave, and also that the motion through wrx simultaneously with w v x will result in a movement in the line wy x, consequently on emergence a wave is produced vibrating in the plane w x. This plane is however inclined 90° to the original plane of polarization, and on looking down on the cylinder it will be seen that it is turned 90° to the right, a result which must follow from the fact that the right-handed helical ray e s t u v has passed through the crystal more rapidly than the left-handed ray emnopqr, which is retarded by half a wave length. If the upper surface of the crystal were at E F, the plane of polarization would be turned 30° to the right, and at GH the plane would be turned 60° to the right. The rotation of the ray is dependent on the wave length of the light and also on the refracting medium producing the rotation.