The scattering of radiation in the presence of weak magnetic fields can give rise to coherence or interference phenomena that will profoundly affect the frequency, geometric, and polarization properties of the scattering event. In this paper we discuss and illustrate some of the features of the coherence phenomena associated with the scattering redistribution for the normal Zeeman triplet. The frequency dependent as well as the frequency independent scattering function is considered in a linear polarization basis. In addition we illustrate some properties of this redistribution function in the Stokes representation. Since the primary purpose of this paper is to demonstrate the nature of some of the properties of the coherence problems, that might be important in the interpretation of magnetic fields from polarization measurements of scattered radiation, it has been necessary in this initial work to neglect several features of the problem which are noted in the paper and are currently under investigation.