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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.
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 bi-quartz consists of two semicircular plates of quartz placed so as to have a common diameter. The one is right-handed, 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, plane-polarised 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: L is the lamp, A the slit, and C the collimating lens. The parallel rays fall on the polarising Nicol N and the bi-quartz B. They then traverse the tube T containing the active rotatory substance and the analysing Nicol N', falling on the lens M which forms an image of the bi-quartz on the slit S of the small direct-vision spectroscope. If we wish to do without the spectroscope, we can remove both it and the lens M and view the bi-quartz either with the naked eye or with a lens or small telescope adjusted to see it distinctly. If we use the single quartz, we can substitute it for the bi-quartz, and focus the eye-piece of the telescope to see the first slit A distinctly, and thus observe the tint of passage.
The quartz plate may be put in both cases at either end of the tube T. If it be placed as in the figure, and the apparatus is to be used to measure the rotation produced by some active substance, the tube should in the first instance be filled with water, for this will prevent the necessity of any great alteration in the adjustment of the lens M or in the focussing of the telescope, if the lens be not used, between the two parts of the experiment.
The mode of adjusting the Nicols has been already described.
The light should traverse the quartz parallel to its axis, and this should be at right angles to its faces. This last adjustment can be made by the same method as was used for placing the axis of the Nicol in the right position, provided the maker has cut the quartz correctly. In practice it is most convenient to adjust the quartz by hand, until the bands formed are as sharp and clear as may be.
Care must be taken that each separate piece of the apparatus is securely fastened down to the table to prevent any shake or accidental disturbance.
If a lens is used at M, it is best to have it secured to the tube which carries the analysing Nicol, its centre being on the axis of this tube; by this means it is fixed relatively to the Nicol, and the light always comes through the same part of the lens. This is important, for almost all lenses exert a slight depolarising effect on light, which differs appreciably in different parts of the lens. For most purposes this is not very material, so long as we can be sure that the effect remains the same throughout our observations. This-assurance is given us, provided that the properties of the lens are not altered by variations of temperature, if the lens-be fixed with reference to the principal plane of the analyser, so that both lens and analyser rotate together about a common axis.
One other point remains to be noticed. If equality of tint be established in any position, and the analyser be then turned through 180°, then, if the adjustments be perfect, there will still be equality of tint To ensure accuracy we should take the readings of the analysing Nicol in both these positions. The difference between the two will probably not be exactly 180°; this arises mainly from the fact that the axis of rotation is not accurately parallel to the light. The mean of the two mean readings will give a result nearly free from the error, supposing it to be small, which would otherwise arise from this cause.
To attain accuracy in experiments of this kind needs considerable practice.
(1) Set up the apparatus and measure the rotation produced by the given plate of quartz.
(2) Make solutions of sugar of various strengths, and verify the law that the rotation for light of given wave-length varies as the quantity of sugar in a unit of volume of the solution.
Enter results thus: -
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