Quarter-wave retarders (QWR) that employ TIR and interference of light in a transparent thin-film coating at the base of a prism are presented. Explicit equations that guide the optimal design are provided. The optimal refractive index and normalized thickness of QWR coatings on glass and ZnS prisms are determined as functions of the internal angle of incidence from 45o to 75o. An achromatic QWR that uses an Si3N4-coated N-BK10-Schott glass prism is also presented with retardance error of 50 dB) over the 4-12 m IR spectral range is achieved using a SWS 1-D PCL of ZnTe embedded in a ZnS cube...