124.] COLOURS OF POLARIZED LIGHT. vibration of the polarized ray. 239 Let the line A B. (fig 103 a) re E FIG. 103 a. H present the plane of vibration of a polarized ray traversing a thin film of a doubly refracting crystal at the point m, the surface of the crystal being supposed to lie in the plane of the paper let the intensity of the polarized light, or the amplitude of a wave, be represented by the length m n, this ray, in passing through the crystal, will be decomposed into two rays vibrating in the planes E F and G H, and the amplitude of the two component waves will be represented by the lengths mo and m p. If the thickness of the crystal is such that one of the rays is retarded by one wave length, or any number of whole wave lengths behind the other during the passage of the light through the crystal, on emergence B FIG. 103 b. A. m H an ether particle at m will be moved in the direction m o, simultaneously with the motion of another ether molecule in the direction m p. When these two rays meet the analyser, the vibration plane of which is indicated by the line C D (fig. 103b), each of the rays vibrating in the planes E F and G н, may be resolved into two vibrations in planes at right angles to one another, one component of each being parallel to the plane a B, and the other to c D. The components parallel to A B cannot be transmitted by the analyser c in the crossed position; and although the components m q and mr are in the plane of the analyser, yet no light is transmitted, as interference takes place. We have seen that an ether particle at m will be moved B in the direction m o simultaneously with the motion of a particle along mp; therefore, in the plane c D a particle will move from m to q simultaneously with the motion of one from m to r, consequently a particle at m will be solicited by two equal and opposite 240 COLOURS OF POLARIZED LIGHT. [124. forces, and no motion can result. If the doubly refracting crystal be of such a thickness that one ray is retarded by half a wave length, or an uneven number of half wave lengths behind the other, then, on emergence of the light an ether particle will move from o tom, at the same time that one moves from m to p, and in the case of the components in the plane c D a particle will move from q to m simultaneously with one from m to r; these being in the same direction will not interfere, but will be transmitted through the analyser. So when the polarizer and analyser are crossed, and the rays transmitted by the crystals differ by a wave length, or whole numbers of wave lengths, no light passes the analyser; whereas, when the rays differ by half a wave length, or an uneven number of half wave lengths, light is transmitted. In the next place, let us consider the case of the polarizer and analyser being parallel, the crystal remaining in the same E FIG. 103 C. A,C m H F position as previously. In fig. 103 c the planes of vibration of both polarizer and analyser will be represented by the line A B, and the components of the polarized ray will be represented as before by mo and mp. If the thickness of the crystal be such that one of the component rays is retarded by one wave length, or a whole number of wave lengths, then, as before, an ether particle will move from m to o simultaneously with the motion of one from m to p. These rays meeting with the analyser are each decomposed into two vibrations at right angles to one another, one of each being parallel to C D and the other perpendicular to it. The latter cannot, of course, pass the analyser, whilst the components parallel to C D are each represented by m s, and in this case, the vibrations mo and m p will combine to move a particle at m in the direction m s, so no interference will take place, and the light will be transmitted by the analyser. If the crystal be of such a thickness that one ray is retarded by half a wave length, or an uneven number of half wave lengths, then a particle will move from o to m simultaneously with the motion of one from m top; the components of those which are parallel to CD will be represented by ms, but they are equal and opposite, therefore interference results. So when the polarizer and analyser are parallel, and the rays transmitted by the crystal differ by a wave length, or whole number of wave lengths, no B'D 124.] COLOURS OF POLARIZED LIGHT. 241 interference takes place, and light is transmitted by the analyser; whereas, when they differ by half a wave length, or an uneven number of half wave lengths, there is interference, and no light passes. It will easily be seen (especially by the use of diagrams similar to those above described, and which the student may construct for himself) that the rotation of the analyser or polarizer will cause partial interference; thus in rotating the analyser or polarizer through 90° complete interference will be gradually replaced by no interference, and in continuing the rotation through the next quadrant the interference will increase to a maximum. What has been stated in the previous paragraphs is obviously only applicable to monochromatic light, or light of one refrangibility or wave length, for interference cannot take place between waves of different lengths. A very instructive experiment may be performed by making two selenite plates, one of which, when yellow sodium light is employed, retards one of the rays an even number of half wave lengths, and the other plate retarding one of the rays an uneven number of half wave lengths. The first, when examined by a polariscope, will appear dark when the field is dark, and light when the field is light, and the second will be bright on a dark field when polarizer and analyser are crossed, and dark on a bright field when they are parallel. When white light is used, complete interference can only ensue with light of one particular wave length, but partial interference takes place with light of the neighbouring refrangibilitics. This is readily recognised by examining the light which has passed through the polariscope by means of a spectroscope, when it will be noticed that a band crosses the spectrum which is quite black in the centre, and shaded off towards the edges. The light which leaves the polariscope is therefore complementary to that which is represented by the dark band in the spectrum. The thinnest film will produce interference with the shortest waves, so that the violet is the first to disappear when a piece of selenite in the form of a thin wedge is employed. At places slightly thicker the blue waves will interfere, and so on, through the spectrum. In the first series the rays transmitted by the film differ by half a wave length (or a whole wave length, according to the position of the analyser), so that when examined with white light the extreme end of the wedge will appear nearly white; as the thickness increases the light will appear yellowish brown passing into red; when this happens the maximum interference is in the green; 242 COLOURS OF POLARIZED LIGHT. [124. a still thicker part of the wedge the colour will be bluish-green, when the interference takes place in the red. When interference takes place beyond the extreme red end of the spectrum, the light transmitted by the analyser will be nearly white, for since the wave length of the extreme red is about double that of the light of the extreme violet, a piece of selenite, which retards a red ray one half wave length, will retard the blue ray two half wave lengths, there will, therefore, be no interference of the blue rays; on further increasing the thickness, a black band will be observed at the blue end of the spectrum when one ray is retarded three half wave lengths behind the other, and on still increasing the thickness of the selenite this band will travel along the spectrum, but before it has reached the red end a second band appears, which is produced when one of the blue rays is retarded five half wave lengths, the ray of less refrangible light being retarded only three. Further increase of thickness of the crystal will develope more black bands in the spectrum, until ultimately the suppressed light is so equally distributed over the spectrum that the remaining light, when combined, appears white. The thinnest plate of selenite that transmits red light when the polarizer and analyser are crossed (that is, when there is interference in the green part of the spectrum), is about four hundredths of a millimetre, and in the spectrum of the light transmitted there is one black band in the green; a plate of the thickness of three quarters of a millimetre transmits white light in all positions of the analyser, but when polarizer and analyser are crossed or parallel, six or seven black bands appear in the spectrum, the transmitted white light is therefore composed of the remainder of the spectrum. The succession of tints caused by increasing the thickness of the wedge follows the same order as the colours of Newton's rings. That the colour, when the polarizer and analyser are crossed, is complementary to that observed when they are parallel, is well shown by substituting a rhombohedron of calcareous spar for the analysing plate, so as to obtain two images of the polarized beam: on turning the spar round, the two images will be seen tinged of complementary hues in all parts of the revolution; and if the two images be allowed to overlap a little, the overlapping portions will in all positions be white. The production of these colours is not confined to crystallized minerals, but they are obtainable in a less degree with substances of animal origin, such as quill, horn, or membrane. (125) Coloured Rings.-If the plate interposed between the 125.] COLOURED RINGS OF POLARIZED LIGHT. 243 polarizing and analysing surfaces be cut from an uniaxal crystal in a direction perpendicular to that of the optic axis, the transmitted ray will still be coloured, but the phenomenon is different, and still more beautiful. A series of coloured rings will be observed, intersected by a cross, which, in one position of the analysing plate will be white (fig. 104, 1); on causing the analyser to rotate FIG. 104. through an arc of 90°, the white cross will be succeeded by a black one (fig. 104, 2), and the rings of colours will exhibit tints complementary to those before observed; at the next quadrant the colours of the first reappear, whilst at the succeeding quadrant they are again complementary. Rotation of the crystal on its own axis produces no change in the tints or in the position of the cross. The general explanation of these facts is not difficult:If P P (fig. 105) be a section of the interposed plate, I the diverging polarized beam, T T the tourmaline, u v w a section of the screen on which the image is received, it is obvious that the rays, 1 v, which tra verse the plate P P, parallel to the optic axis, will suffer no change; but all the lateral rays, IU, Iw, which fall upon PP more or less ob P FIG. 105. T W T liquely, according to their distance from the line I v, will be doubly refracted, the two rays being polarized in planes at right angles to one another; one of each these doubly refracted rays will thus be retarded upon the other, and as soon as the two rays are brought into the same plane by the action of the analysing tourmaline, they interfere, and give rise to the brilliant |