Page 194 - A Practical Introduction to Optical Mineralogy
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THE  BIAXIAL  INDICATRIX
                          (a)       a                                                                Anisotropic crystals transmit light with different velocities in different
                                                                                                   directions, and the ray velocity surface of such a crystal is an ellipsoid,
                                                                                                   which  may be of two principal geometric types,  biaxial  and  uniaxial.
                             a'
                                                                                                   4.4  The biaxial indicatrix (triaxial ellipsoid)
                                                                                I
                                                                                I                  Anisotropic  crystals  belonging  to  the  orthorhombic,  monoclinic  and
                                                                                                   triclinic systems are biaxial, and are characterised by having three prin-
                                                                                                   cipal refractive indices and two optic axes. The relationship between the
                                                                                                   refractive  indices  can  best  be seen  in  a  biaxial  indicatrix,  which  is  a
                                                                                                   triaxial  ellipsoid  possessing  three  planes  of symmetry,  with  the  three
                                                                                                   principal  refractive  indices  equal  to  the  three  main  semi-axes  of the
                                                                                                   ellipsoid. These three refractive indices are given the symbols n. , n p and
                                                                                                   n y, and in all biaxial crystals n y is greater than n p which is greater than n.
                                                                                                   (i.e. n y > n p > n. ). In positive biaxial crystals n p is closer in value ton.,
                                                                d
                                                                                                   whereas in negative biaxial crystalsnp is closer in value ton y.  Where n p is
                                                                                                   exactly  intermediate between n.  and n y it  is  impossible to  determine
                                                                                                   whether the crystal  is  positive or negative (since  2V would be exactly
                                                                                                   90°).  Through  any  biaxial  indicatrix  two  cross  sections  can  be drawn
                                                                                                   which are true circles with a radius of n p,  because n p is  intermediate in
                                                                                                   size between n. and n y. The position occupied in the indicatrix by these
                          (b)       a
                                                                                                   two circular sections depends on the relationship of n p ton.  and n y,  i.e.
                                                                                                   whether n p is  nearer n.  or n y in  value (Figs 4.3  &  4).
                                                                                             ~2V---._
                             a'
                                                                                           OA          OA
                                                                                            ,   n-v  =  Bxa   1



                                                                   VI
                                                                                                            cs


                                                                                                            cs
                                                                d


                                                     d'


                                                                                       Figure  4.3  Positive  biaxial indicatrices.   Figure 4.4  Negative  biaxial indicatrices.
                      Figure 4.2  Refraction of light at a plane surface (a) H uygenian construction for
                                                                                       OA, optic axis;  CS, circular section;   OA, optic axis;  CS, circular section;
                      several rays (b) simplified version of (a).
                                                                                       Bxa,  acute bisectrix; Bx 0 ,  obtuse  bisectrix.   Bxa,  acute bisectrix; Bx 0 ,  obtuse bisectrix.
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