Discovery of ambiguity in the traditional definitions of angle of diffraction and glancing angle

This paper reports on the discovery of ambiguity in the traditional definitions of the 'Angle of diffraction' in Physical/Wave optics and 'Glancing angle' in X-ray crystallography. Just like the 2005 discovery by the author regarding the ambiguity in the traditional definitions of angles of incidence, reflection and refraction, the traditional definitions of the aforesaid two angles have also been found to be ambiguous. The long-running definition of angle of diffraction in Physical/Wave optics does not have any parity with the definitions of angles of incidence, reflection, and refraction in Geometrical optics, in each of which the direction of the positive unit normal to the reflecting surface (surface of discontinuity) at the point of incidence is one of the two directions to be considered in defining the angle. Similarly the traditional definition of the Glancing/Grazing angle in X-ray crystallography is in conflict with the fundamental definition of angle in geometry. With a view to getting rid of the ambiguity present in the traditional definitions of 'Angle of diffraction' and 'Glancing/Grazing angle', as well as to enhance and sophisticate the relevant field of study, unambiguous definitions of both these two angles have been offered in this paper.