The cumulative retardance Delta(t) introduced between the p and the s orthogonal linear polarizations after two successive total internal reflections (TIRs) inside a right-angle prism at complementary angles phi and 90 degrees - phi is calculated as a function of phi and prism refractive index n. Quarter-wave retardation (QWR) is obtained on retroreflection with minimum angular sensitivity when n=(sqr rt 2+1)(1/2)=1.55377 and phi =45 degrees. A QWR prism made of N-BAK4 Schott glass (n=1.55377 at lambda=1303.5 nm) has good spectral response (<5 degrees retardance error) over the 0.5-2 microm visible and near-IR spectral range. A ZnS-coated right-angle Si prism achieves QWR with an error of < +/- 2.5 degrees in the 9-11 microm (CO(2) laser) IR spectral range. This device functions as a linear-to-circular polarization transformer and can be tuned to exact QWR at any desired wavelength (within a given range) by tilting the prism by a small angle around phi =45 degrees. A PbTe right-angle prism introduces near-half-wave retardation (near-HWR) with a < or =2% error over a broad (4< or =lambda< or =12.5 microm) IR spectral range. This device also has a wide field of view and its interesting polarization properties are discussed. A compact (aspect ratio of 2), in-line, HWR is described that uses a chevron dual Fresnel rhomb with four TIRs at the same angle phi =45 degrees. Finally, a useful algorithm is presented that transforms a three-term Sellmeier dispersion relation of a transparent optical material to an equivalent cubic equation that can be solved for the wavelengths at which the refractive index assumes any desired value.