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The theory of these, as has been stated, all turns on the fact that it is comparatively easy to determine when two objects placed side by side are equally illuminated, the illumination being faint.
Suppose, then, we view through a small telescope or eye-piece placed behind the analyser a circular hole divided into two parts across a diameter, and arranged in such a way that the planes of polarisation of the light emerging from the two halves are inclined to each other at a small angle. For one position of the analyser one half of the field will be black, for another, not very different, the other half will be black, and for an intermediate position the two halves will have the same intensity. The analyser can be placed with the greatest nicety in the position to produce this. If now the planes of polarisation of the light from the two halves of the field be each rotated through any the same angle and the analyser turned until equality of shade is re-established, the angle through which the analyser turns measures the angle through which the plane of polarisation has been rotated.
In nearly all cases homogeneous light must be used for accurate work. Excellent results can be obtained by placing a bead of sodium on a small spoon of platinum gauze just inside the cone of a Bunsen burner, and then allowing a jet of oxygen to play on the gauze.
Lord Rayleigh has found that a good yellow light is given by passing the gas supplied to a Bunsen burner through a small cylinder containing a finely divided salt of sodium, keeping the cylinder at the same time in a state of agitation, while Dr. Perkin passes the gas over metallic sodium in an iron tube which is kept heated. The brilliancy of the light is much increased by mixing oxygen with the coal gas as in the oxyhydrogen light.
Whenever a sodium flame is used, it is necessary that the light should pass through a thin plate of bichromate of potassium, or through a small glass cell containing a dilute solution of the same salt, to get rid of the blue rays from the gas.
In almost all cases the half-shadow arrangement may be attached to either the polariser or the analyser. If the latter plan be adopted, it must, of course, turn with the analyser, and this is often inconvenient; the other arrangement, as shown in fig. 40, labours under the disadvantage that the telescope requires readjusting when the tube with the rotating liquid is introduced.
We will mention briefly the various arrangements which have been suggested(1) for producing a half-shadow field, premising, however, that as the sensitiveness depends both on the brightness of the light and the angle between the planes of polarisation in the two halves of the field, it is convenient to have some means of adjusting the latter. "With a bright light this angle may conveniently be about 2°.
It is also important that the line of separation between the two halves should be very narrow, and sharp, and distinct.
(1) Jellett's prism:
The ends of a long rhomb of spar are cut off at right angles to its length, and then the spar cut in two by a plane parallel to its length and inclined at a small angle to the longer diagonal of the end-face. One half is turned through 180° about an axis at right angles to this plane, and the two are reunited.
If a narrow beam of parallel rays fall normally on one end of such an arrangement, the ordinary rays travel straight through without deviation, but their planes of polarisation in the two halves are inclined to each other at a small angle. The extraordinary rays are thrown off to either side of the apparatus, and if the prism be long enough and the beam not too wide, they can be separated entirely from the ordinary rays and stopped by a diaphragm with a small circular hole in it through which the ordinary rays pass.
(2) Cornu's prism:
A Nicol or other polarising prism is taken and cut in two by a plane parallel to its length. A wedge-shaped piece is cut off one half, the edge of the wedge being parallel to the length of the prism, and the angle of the wedge some 3°. The two are then reunited, thus forming two half-Nicols, with their principal planes inclined at a small angle. The light emerging from each half is plane-polarised, the planes being inclined at a small angle.
Both of these suffer from the defects that the angle between the planes of polarisation is fixed and that the surface of separation of the two halves being considerable, unless the incident light is very strictly parallel, some is reflected from this surface, and hence the line of separation is indistinct and ill-defined.
(3) Lippich's arrangement:
The polariser is a Glan's prism. Lippich finds this more convenient than a Nicol, because of the lateral displacement of the light produced by the latter.
A second Glan's prism is cut in two by a plane parallel to its length, and placed so that half the light from the first prism passes through it, while the other half passes at one side. The first prism is capable of rotation about an axis parallel to its length, and is placed so that its principal plane is inclined at a small angle, which can be varied at will, to that of the half-prism. The plane of polarisation of the rays which emerge from this half-prism is therefore slightly inclined to that of the rays which pass to one side of it, and this small angle can be adjusted as may be required.
This arrangement also has the disadvantage that the surface of separation is large, and therefore the line of division is apt to become indistinct.
(4) Lippich has used another arrangement, which requires a divided lens for either the telescope or collimator, and is, in consequence, somewhat complicated, though in his hands it has given most admirable results.
All these four arrangements can be used with white light, and are therefore convenient in all cases in which the rotatory dispersion produced by the active substance, due to variation of wave-length in the light used, is too small to be taken into account.
(5) Laurent's apparatus:
The polariser is a Nicol followed by a half-wave plate for sodium light, made of quartz or some other crystal
If quartz cut parallel to the axis be used, the thickness of the plate will be an odd multiple of 0.0032 cm. One of the axes of this plate is inclined at a small angle to the principal plane of the Nicol. The plate is semicircular in form and covers half the field - half the light passes through it, the other half to one side. The light on emerging from the plate is plane-polarised, and its plane of polarisation is inclined to the axis of the quartz at the same angle as that of the incident light, but on the opposite side of that axis. We have thus plane-polarised light in the two halves of the field - the angle between the two planes of polarisation being small.
And, again, by varying the angle between the axis of the quartz and the plane of polarisation of the incident light, we can make the angle between the planes of polarisation in the two halves of the field anything we please; but, on the other hand, since the method requires a half-wave plate, light of definite refrangibility must be used.
(6) Poynting's method:
Poynting suggested that the desired result might be obtained by allowing the light from one half the field, after traversing a NicoFs prism, to pass through such a thickness of some rotatory medium as would suffice to produce in its plane of polarisation a rotation of 2° or 3°. If quartz cut perpendicular to the axis be used, this will be about 0.01 cm for sodium light. A plate of quartz so thin as this being somewhat difficult to work, Poynting suggested the use of a thicker plate which had been cut in two; one half of this thicker plate is reduced in thickness by about 0.01 cm, and the two pieces put together again as before; the light from one half the field traverses 0.01 cm of quartz more than the other, and hence the required effect is produced. This works well, but it is important that the light should pass through both plates of quartz parallel to the axis, otherwise elliptic polarisation is produced. Moreover, the difficulty of obtaining a plate of quartz 0.01 cm thick is not really very great.
Another suggestion of Poynting's was to use a glass cell with a solution of sugar or other active substance in it A piece of plate glass of 3 or 4 mm. in thickness is placed in the cell, the edge of the plate being flat and smooth. The polarised light from half the field passes through the glass plate, that from the other half traverses an extra thickness of some 3 or 4 mm. of sugar solution, which rotates it through the required angle. This method has an advantage over the quartz that we are able to adjust the angle between the planes of polarisation in the two halves of the field by varying the strength of the solution. Its simplicity is a strong point in its favour. It has the disadvantage that it is rather difficult to get a clear sharp edge, but care overcomes this.
Of course the adjustments necessary in the position of the Nicols, the method of taking the readings, &c., are the same as those in the last section.
Set up a half-shadow polarimeter and measure the rotation produced in active solutions of various strengths, determining the relation between the strength of the solution and the rotation.
Enter results as in preceding section.
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