Refraction and Double Refraction

Natural Optical Gyration.

Double refraction is not the only optical effect exerted by crystals. The symmetrical proper ties of a crystal are of two different kinds, corresponding to rotation and reflection respectively. Most crystals have some symmetry elements of both types, but there are some which only have rotations, so that the crystal is not identical with its mirror image. The simplest geometrical form possessing this peculiarity is the screw, which cannot be superposed on its mirror image, and we therefore liken this type of crystal to a screw. Quartz is such a substance, and there exist two types of quartz crystals, which we may call right- and left-handed. Now circularly polarized light has the same quality of a screw, and we should therefore expect that a right-handed quartz crystal would react differently to right- and left-handed circularly polarized light respectively. It is in fact found that the wave-velocities are different, and this is the basis of the theory of optical gyration.

Let us suppose that and ni are the refractive indices for the two types of circularly polarized light of frequency v. Then the right-handed wave will be Suppose that at the plane z=o we have light polarized along the direction x. This is given by simply adding these two solutions together, and then at any value of z we shall have This means that at the point z we can regard the light as plane polarized in a direction inclined to x at angle The phenomenon is actually observed by sending plane polarized light through the medium and seeing how an analyzing nicol must be placed in order to extinguish the light. The gyrational constant

is the rotation produced by a thickness of i cm. of the substance.

In quartz the gyration is very strong, being 217° per cm. for yellow light, but is complicated by double refraction of the uniaxial type, and it is only for light going very nearly along the crystal axis that it can be observed. There are also crystals of the regular system which exhibit the effect, for example sodium chlorate, and here it is present for all directions. It is also shown by liquids when their molecules contain a chemically asymmetric atom ; such a liquid is isotropic in that all directions are equiva lent, but is not, molecularly speaking, identical with its mirror image, and so it can and does refract the two types of circularly polarized light differently. Since many sugars contain an asym metric carbon atom, measurement of the gyration is a very convenient method of estimating the strength of a sugar solution, and great practical use is made of it.