Add to ORKGAbstract: Explicit equations are derived for the design of quarter-wave retarders (QWR) that exploit total internal reflection (TIR) and interference of light in a transparent thin-film coating at the base of a prism. 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 45D to 75.D An achromatic retarder that uses TIR by a Si3N4-coated N-BK10-Schott glass prism is also presented that achieves exact QWR at two wavelengths (409 and 500 nm) and exhibits a retardation error of < 1.5o for wavelengths 375 ≤ λ ≤ 550 nm in the near-UV and the violet-blue-green part of the visible spectrum