In general a crystal may exhibit three principal refrective indixcies corresponding to three mutually orthogonal axis. In some of the crystals, there may be one particular axis, say z axis such that if the light is propagating along this axis then the two mutually orthogonal waves may be same. Such axis is called as the optics axis and the crystal is termed as uniaxial crystal. In a uniaxial crystal, the propagation of light along the optics axis or along the z axis is independent of the state of polarization, just like the isotropic system. The refractive index in such situation is denoted as n_o. In case if the light is traveling along x (or y) direction, other than optics axis then the refractive indices will be different for two mutually orthogonal polarization. The light polarized along y direction (or x) will have refractive index n_o and that of along z direction it is denoted by n_e accordingly the waves are called as ordinary and extraordinary rays.. Suffix e denotes the extraordinary behaviour. In other words, one can say the uniaxial crystals offers two refractive indices n_o and n_e and hence are birefringent material.

•  Propagation of light through birefringent crystal :

Let us consider a uniaxial crystal placed in air. As discussed in the previous module, the radiation falling at an interface may be resolved in two kinds of polarization, viz: in plane polarization and perpendicular polarization. To make the discussion simple, we will consider the normal incidence only. If n_o> n_e, the crystal is called as positive crystal and if n_o< n_e, the crystal is called as negative crystal.

Case I:Let us consider the first case when the optics axis is perpendicular to the interface formed by the uniaxial crystal and the air as shown in Fig.2. In this case, the refractive indicies for both polarization is same and is given by n_o.