Page 195 - A Practical Introduction to Optical Mineralogy

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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