In [Fig. 32] is given a more detailed illustration of the action of the rays of light. The film of balsam is represented as enlarged and of the thickness bb. Draw the perpendiculars represented by the dotted lines n₁ nʹ₁, n₂ nʹ₂, n₃ nʹ₃ and n₄ nʹ₄. In passing into the prism at m both refracted rays are bent towards the normal m nʹ₁. The degree of deflection depends on the refractive index of the two rays 1.52 and 1.66 respectively. The refractive index of the extraordinary ray in calcspar being 1.52, and in Canada balsam 1.54, it suffers but little disturbance in passing from one to the other. On the other hand the balsam, being considerably less refractive for the ordinary ray than the calcspar, causes that ray to diverge outwards from the normal o nʹ₂, and to such a degree as to suffer total reflection. The critical angle, that is the angle at which a ray issuing from a more refractive into a less refractive medium, emerges just parallel to the bounding surfaces, depends on the relative index of refraction. In the case under consideration the ratio for balsam and spar is 1.54/1.66 = 0.928 = sin 68°. Therefore the limiting value of m o n₃ so that m o may just emerge in the direction od is 68°. If now mo were parallel to o d the angle m o n, would be just 68°, being opposite b a d. which has been ground to 68° in the construction of the prism. But in passing into the prism, m o is refracted so that the angle m o n₃ is greater than b a d. It is therefore always certain that by grinding b a d to 68° the ordinary ray m o will be with certainty entirely thrown out in every case. In respect of the analyzing nicol the following additional observations will be found useful. In all uniaxial crystals there are two directions at right angles to each other, one of greatest and one of least resistance to the propagation of luminous vibrations. These planes are in the direction of the principal axis and at right angles thereto. Only light vibrating in these two directions can be transmitted through calcspar; and all incident light propagated by vibrations in a plane at any other angle to the principal section is resolved into two such component rays. But the velocities of transmission in the two directions are unequal, that is, the refractive index of the spar for the two rays is different. If the analyzing nicol be so adjusted as to receive the emergent light from the polarizer when the corresponding planes of the two prisms are coincident when extended, the emergent extraordinary ray falling into a plane of the same resistance as that it had just left is propagated through the second nicol with the same velocity that it passed the first one. It is therefore similarly refracted. If, however, the two prisms be so arranged that corresponding planes cross then the extraordinary ray falls into a plane which it traverses with greater velocity than it had before and is accordingly refracted and takes the course which ends in total reflection at the film of balsam. No light therefore can pass through the prism in that position. If any other substance, as for instance a solution of sugar, capable of rotating a plane of polarized light, be interposed between the two nicols the effect produced is the same as if the analyzer had been turned to a corresponding degree. When the analyzer is turned to that degree the corresponding planes again coincide and the light passes. This is the principle on which the construction of all polarizing instruments is based.[36]
63. The Polariscope.—A polariscope for the examination of solutions of sugar consists essentially of a prism for polarizing the light, called a nicol, a tube of definite length for holding the sugar solution, a second nicol made movable on its axis for adjustment to the degree of rotation and a graduated arc for measuring it. Instead of having the second nicol movable, many instruments have an adjusting wedge of quartz of opposite polarizing power to the sugar, by means of which the displacement produced on the polarized plane is corrected. A graduated scale and vernier serve to measure the movement of the wedges and give in certain conditions the desired reading of the percentage of sugar present. Among the multitude of instruments which have been devised for analytical purposes, only three will be found in common use, and the scope of this volume will not allow space for a description of a greater number. For a practical discussion of the principles of polarization and their application to optical saccharimetry, the reader may conveniently refer to the excellent manuals of Sidersky, Tucker, Landolt, and Wiechmann.[37]
64. Kinds of Polariscopes.—The simplest form of a polarizing apparatus consists of two nicol prisms, one of which, viz., the analyzer, is capable of rotation about its long axis. The prolongation of this axis is continuous with that of the other prism, viz., the polarizer. The two prisms are sufficiently removed from each other to allow of the interposition of the polarizing body whose rotatory power is to be measured.
For purposes of description three kinds of polarimeters may be mentioned.
1. Instruments in which the deviation of the plane of polarization is measured by turning the analyzer about its axis.
Instruments of this kind conform to the simple type first mentioned, and are coeteris paribus the best. The Laurent, Wild, Landolt-Lippich, etc., belong to this class.
2. Instruments in which both nicols are fixed and the direction of the plane of polarized light corrected by the interposition of a wedge of a solid polarizing body.
Belonging to this class are the apparatus of Soleil, Duboscq, Scheibler, and the compensating apparatus of Schmidt and Haensch.
3. Apparatus in which the analyzer is set at a constant angle with the polarizer, and the compensation secured by varying the length or concentration of the interposed polarizing liquid.
The apparatus of Trannin belongs to this class.