It is well known that in bi-anisotropic media, e.g., chiral media, gyrotropic media, the polarization vector of linearly polarized waves undergoes rotation. Upon reflection, the returning waves show different effects: In gyrotropic media the rotation is enhanced, while in chiral media it is unraveled and annulled. In general, these properties are not necessarily intrinsic to the media involved but depend on the reflection mechanism, as shown below. It must be emphasized at the outset that in the present study external mirroring mechanisms only are considered, so that the reflection at the interface separating the active medium (chiral or gyrotropic) from the external domain does not enter the discussion. Strictly speaking, the effect of these interfaces cannot be ignored, except in special cases. However, where our approach is valid, it leads to a simple consistent and non-trivial picture of the effects involving returned waves in the presence of external mirror mechanisms. Inasmuch as this analysis is of importance for practical applications, e.g., in ocular glucose polarimetry measurements, and because the mathematics involved here is minimal, the subject appears to be timely and worthwhile. Two different mirror mechanisms are shown to exist: The simple, conventional mirror mechanism, henceforth referred to as "reflection", and a different mechanism referred to as "retrodirection". The simplest example for retrodirection is a wave turned around by an optical fiber. A similar retrodirection effect occurs when the wave is turned around by a set of two conventional reflectors. In non-chiral non-gyrotropic media the two categories lead to identical effects, and the distinction is superfluous. Presently we consider the effect of such reflection and retrodirection mirroring mechanisms on the total rotation of the polarization vector of a wave undergoing a round trip in chiral, and in gyrotropic media. It is shown that for the case of reflection and chiral media, the rotation is canceled, while in the presence of a retrodirecting mirror, the rotation is enhanced. For gyrotropic media we have the opposite situation: A reflector will induce enhanced rotation, while a retrodirector will cause the total rotation to vanish. Various situations are considered below, involving mirroring mechanisms. Provided we stay within the limitations of the present model, simple well-known considerations relevant to the Fresnel theory of reflection of plane waves by plane interfaces, as well as simple geometrical observations, suffice for analyzing the problems and drawing the conclusions.