  Scanning tunneling spectroscopy applied to the high-$T_{c}$ cuprates has
revealed significant spatial inhomogeneity on the nanoscale. Regions on the
order of a coherence length in size show variations of the magnitude of the
superconducting gap of order $\pm20%$ or more. An important unresolved question
is whether or not these variations are also present in the bulk, and how they
influence superconducting properties. As many theories and data analyses for
high-$T_{c}$ superconductivity assume spatial homogeneity of the gap magnitude,
this is a pressing question. We consider the far-infrared optical conductivity
and evaluate, within an effective medium approximation, what signatures of
spatial variations in gap magnitude are present in various optical quantities.
In addition to the case of d-wave superconductivity, relevant to the high-$T_c$
cuprates, we have also considered s-wave gap symmetry in order to provide
expected signatures of inhomogeneities for superconductors in general. While
signatures of gap inhomogeneities can be strongly manifested in s-wave
superconductors, we find that the far-infrared optical conductivity in d-wave
is robust against such inhomogeneity.
