Measurement of optical refractive indices or birefringence

As discussed in section 9.2.1, the refractive index of a substance depends on the polarisabilities of its basic units. The Lorentz-Lorenz equation derived there as equation (9.9) links the refractive index n and the polari-sability a of the structural units in any isotropic medium. It ean be written in the slightly simpler form 

Ao is the number of structural units per unit volume and the polarisa-bility a relates the electric dipole p induced in a unit to the applied electric field E. For isotropic units, as assumed in section 9.2.1, 

If the units are anisotropic, a becomes a second-rank tensor [a ] (see the appendix) in this equation and it is then assumed that the Lorentz-Lorenz equation can be modified to read 

The refractive index thus depends on the average value of a,-,-, which depends on the anisotropy of the polarisability and the degree of orientation of the sample. It is shown below that, for uniaxial orientation with respect to OZ3 (for which wj = 2 = t) and a cylindrical polarisability tensor with low asymmetry. 

A specially oriented (hypothetical) sample of a polymer has one half of its structural units oriented with their axes parallel to the draw direction and the other half oriented with their axes uniformly distributed in the plane normal to the draw direction. If the birefringence of this sample is 0.02, calculate the birefringence of a fully uniaxially oriented sample. 

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