  The phenomenon of Faraday rotation of linearly polarized synchrotron emission
in a magneto-ionized medium has been understood and studied for decades. But
since the sense of the rotation itself is irrelevant in most contexts, some
uncertainty and inconsistencies have arisen in the literature about this
detail. Here, we start from basic plasma theory to describe the propagation of
polarized emission from a background radio source through a magnetized, ionized
medium in order to rederive the correct sense of Faraday rotation. We present
simple graphics to illustrate the decomposition of a linearly polarized wave
into right and left circularly polarized modes, the temporal and spatial
propagation of the phases of those modes, and the resulting physical rotation
of the polarization orientation. We then re-examine the case of a medium that
both Faraday-rotates and emits polarized radiation and show how a helical
magnetic field can construct or destruct the Faraday rotation. This paper aims
to resolve a source of confusion that has arisen between the plasma physics and
radio astronomy communities and to help avoid common pitfalls when working with
this unintuitive phenomenon.
