The optical constants of two Ta-Co binary alloys are determined in the spectral range 8.0 nm–22.0 nm using angle-dependent reflectometry (ADR). The extreme-ultraviolet reflectivity (EUVR) profiles of the alloys were measured using highly monochromatized synchrotron radiation from sputtered thin films, each with a nominal thickness of 30.0 nm. Concerning the alloys, the inability to predict the variability of the optical constants' profiles in the vicinity of cobalt’s M-absorption edge region gives unique proof for the need to derive a more complete theory for predicting the optical constants. Markov chain Monte Carlo (MCMC) based Bayesian inferences, and frequency analysis of X-ray reflectivity (XRR) data were utilized to treat the relevant inverse-problem needed for determining the optical constants. An approach is presented here where both the optical constants of the alloys and their surface layers are simultaneously sampled. The results of this report are apropos to strengthen customizing multilayer mirrors (MLMs) and similar ad hoc optical components intended for the extreme-ultraviolet (EUV) spectral range.