Case II . In the second case, the optics axis is parallel to the interface as shown in Fig 4.
For the s wave (having polarization perpendicular to the plane of incidence or to the plane of the paper) the refractive index is n_o (and hence termed as ordinary wave) and the wave front will be spherical wave front as shown in fig 4. But for p wave the refractive index is n_e (or it can be termed as extraordinary wave)and the wave front will be elliptical wave front. It can be drawn by plotting an ellipse with the major axis as c/n_e along the direction of propagation and the minor axis as c/n_o along the optics axis. In this case, s and p wave will develop a relative phase difference while propagating the same length (physical ) in the crystal owing to different refractive indices.