405 CHAPTER XV. POLARISED LIGHT. On the Determination of the Position of the Plane of THE most important experiments to be made with polarised light consist in determining the position of the plane of polarisation, or in measuring the angle through which that plane has been turned by the passage of the light through a column of active substance, such as a solution of sugar, turpentine, or various essential oils, or a piece of quartz. The simplest method of making this measurement is by the use of a Nicol's or other polarising prism. This is mounted in a cylindrical tube which is capable of rotation. about its own axis. A graduated circle is fixed with its centre in the axis of the tube, and its plane at right angles to the axis, and a vernier is attached to the tube and rotates with it, so that the position, with reference to the circle, of a fiducial mark on the tube can be found. In some cases the vernier is fixed and the circle turns with the Nicol. If we require to find the position of the plane of polarisation of the incident light, we must, of course, know the position of the principal plane of the Nicol relatively to the circle. If we only wish to measure a rotation a knowledge of the position of this plane is unnecessary, for the angle turned through by the Nicol is, if our adjustments be right, the angle turned through by the plane of polarisation. For accurate work two adjustments are necessary :— (1) All the rays which pass through the Nicol should be parallel. (2) The axis of rotation of the Nicol should be parallel to the incident light. To secure the first, the source of light should be small; 'See Glazebrook, Physical Optics, chap. xiv. in many cases a brightly illuminated slit is the best. It should be placed at the principal focus of a convex lens ; the beam emerging from the lens will then consist of parallel rays. To make the second adjustment we may generally consider the plane ends of the tube which holds the Nicol as perpendicular to the axis of rotation. Place a plate of glass against one of these ends and secure it in this position with soft wax or cement. The incident beam falling on this plate is reflected by it. Place the plate so that this beam after reflexion retraces its path. This is not a difficult matter; if, however, special accuracy is required, cover the lens from which the rays emerge with a piece of paper with a small hole in it, placing the hole as nearly as may be over the centre of the lens. The light coming through the hole is reflected by the plate, and a spot of light is seen on the paper. Turn the Nicol about until this spot coincides with the hole; then the incident light is evidently normal to the plate- that is, it is parallel to the axis of rotation of the Nicol. If still greater accuracy be required, the plate of glass may be dispensed with, and a reflexion obtained from the front face of the Nicol. This, of course, is not usually normal to the axis, and hence the reflected spot will never coincide with the hole, but as the Nicol is turned, it will describe a curve on the screen through which the hole is pierced. If the axis of rotation have its proper position and be parallel to the direction of the incident light, this curve will be a circle with the hole as centre. The Nicol then must be adjusted until the locus of the spot is a circle with the hole as centre. When these adjustments are completed, if the incident light be plane-polarised, and the Nicol turned until there is no emergent beam, the plane of polarisation is parallel to the principal plane of the Nicol; and if the plane of polarisation be rotated and the Nicol turned again till the emergent beam is quenched, the angle turned through by the Nicol measures the angle through which the plane of polarisation has been rotated. But it is difficult to determine with accuracy the position of the Nicol for which the emergent beam is quenched. Even when the sun is used as a source of light, if the Nicol be placed in what appears to be the position of total extinction, it may be turned through a considerable angle without causing the light to reappear. The best results are obtained by using a very bright narrow line of light as the source-the filament of an incandescence lamp has been successfully employed by Mr. McConnel-as the Nicol is turned, a shadow will be seen to move across this line from one end to the other, and the darkest portion of the shadow can be brought with considerable accuracy across the centre of the bright line. Still, for many purposes, white light cannot be used, and it is not easy to secure a homogeneous light of sufficient brightness. Two principal methods have been devised to overcome the difficulty; the one depends on the rotational properties of a plate of quartz cut normally to its axis; the other, on the fact that it is comparatively easy to determine when two objects placed side by side are equally illuminated if the illumination be only faint. We proceed to describe the two methods. 64. The Bi-quartz. If a plane-polarised beam of white light fall on a plate of quartz cut at right angles to its axis, it has, as we have said, its plane of polarisation rotated by the quartz. But, in addition to this, it is found that the rays of different wavelengths have their planes of polarisation rotated through different angles. The rotation varies approximately inversely as the square of the wave-length; and hence, if the quartz be viewed through another Nicol's prism, the proportion of light which can traverse this second Nicol in any position will be different for different colours, and the quartz will appear coloured. Moreover, the colour will vary as the analysing Nicol, through which the quartz is viewed, is turned round. If the quartz be about 33 mm. in thickness, for one position of the Nicol it will appear of a peculiar neutral grey tint, known as the tint of passage. A slight rotation in one direction will make it red, in the other blue. After a little practice it is easier to determine, even by eye, when this tint appears, than to feel certain when the light is completely quenched by a Nicol. It can be readily shewn moreover that when the quartz gives the tint of passage, the most luminous rays, those near the Fraunhofer line E, are wanting from the emergent beam; and if the quartz have the thickness already mentioned, the plane of polarisation of these rays has been turned through 90°. A still more accurate method of making the observation is afforded by the use of a bi-quartz. Some specimens of quartz produce a right-handed, others a left-handed rotation of the plane of polarisation of light traversing them. A biquartz consists of two semicircular plates of quartz placed so as to have a common diameter. The one is righthanded, the other left. The two plates are of the same thickness, and therefore produce the same rotation, though in opposite directions, in any given ray. If, then, planepolarised white light pass normally through the bi-quartz, the rays of different refrangibilities are differently rotated, and that too in opposite directions by the two halves, and if the emergent light be analysed by a Nicol, the two halves will appear differently coloured. If, however, we place the analysing Nicol so as to quench in each half of the bi-quartz the ray whose plane of polarisation is turned through 90°— that is to say, with its principal plane parallel to that of the polariser-light of the same wave-length will be absent from both halves of the field, and the other rays will be present in the same proportions in the two; and if the thickness of the bi-quartz be about 3.3 mm. this common tint will be the tint of passage. A very slight rotation of the analyser in one direction renders one half red, the other blue, while if the direction of rotation be reversed, the first half becomes blue, the second red. Hence the position of the plane of polarisation of the ray which is rotated by the bi-quartz through a certain definite angle can be very accurately determined. A still better plan is to form the light after passing the analyser into a spectrum. If this be done in such a way as to keep the rays coming from the two halves of the bi-quartz distinct-e.g. by placing a lens between the bi-quartz and the slit and adjusting it to form a real image of the bi-quartz on the slit, while at the same time the slit is perpendicular to the line of separation of the two halves-two spectra will be seen, each crossed by a dark absorption band. As the analysing Nicol is rotated the bands move in opposite directions across the spectrum, and can be brought into coincidence one above the other. This can be done with great accuracy and forms a very delicate method. Or we may adopt another plan with the spectroscope: we may use a single piece of quartz and form the light which has passed through it into a spectrum, which will then be crossed by a dark band; this can be set to coincide with any part of the spectrum. This is best done by placing the telescope so that the cross-wire or needle-point may coincide with the part in question, and then moving the band, by turning the analyser, until its centre is under the cross-wire. Fig. 40 gives the arrangement of the apparatus: Lis the lamp, A the slit, and c the collimating lens. The parallel rays fall on the polarising Nicol N and the biquartz B. They then traverse the tube T containing the active rotatory substance and the analysing Nicol N', falling |