Refractive index of extraordinary light in the uniaxial crystal;

The reflection formulas of the ordinary and extraordinary light are given for determining their reflecting orientation of the wave normal and the light ray.

This paper discusses the conditon on which extraordinary light and Incident light lies to the same side of normal of crystal surface and points out uncertain in some documents

Based on MATLAB,this paper explores extraordinary ray's locus and its features in crystal when uniaxial crystal is turning.

Refraction regularity of extraordinary ray in uniaxial crystal with arbitrarily oriented optical axis;

In the case of optical axis of uniaxial crystal being parallel with the incident plane, the angle of refraction of extraordinary ray are calculated by using Fermat's principle.

In situation the optical axis of an uniaxial crystal lies in the plane of incidence，an equation determining the relationship between the angle of incidenee and that of refractionof extraordinary rays is derived by using Fermat s principle，An illustrative numerical examplefor CaCO_3 crystal is given.

The discussion on the extraordinary ray s total reflection;

The extraordinary ray neither obeys the refractive law,nor has certain index of refraction in nonisotropic medium.

of the extraordinary ray is derived at the interface between two anisotropic mediums by means of Fermat s principle.

The relations among these uniform convexity and uniform smoothness, very smoothness, uniform extreme smoothness and extreme smoothness are studed.

This paper studies the relations among the average uniform convexity, average local uniform convexity, average weak local uniform convexity, uniform smoothness, very smoothness, uniform extreme smoothness and extreme smoothness.

The propagating direction of e-rays in common optical devices-Wollaston s Priam and Nicol s Prism is deduced strictly from the general formulas of the propagating direction of extraordinary rays in single-axle crystals.