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We present x-ray resonant magnetic reflectivity (XRMR) as a very sensitive tool to detect proximity induced interface spin polarization in Pt/FM heterostructures. Different XRMR experiments are carried out and the results are evaluated for their dependence on the magneto-optical depth profile, the photon energy, the optical parameters, and the ferromagnetic material. We demonstrate that a detailed analysis of the reflected x-ray intensity gives insight into the spatial distribution of the spin polarization of a nonmagnetic metal across the interface to a ferromagnetic layer. The evaluation of the experimental results with simulations based on optical data from ab initio calculations provides the induced magnetic moment per Pt atom in the spin-polarized volume adjacent to the ferromagnet. For a series with different ferromagnetic materials consisting of Pt/Fe, $\text{Pt}/{\mathrm{Ni}}_{33}{\mathrm{Fe}}_{67}, \text{Pt}/{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ (permalloy), and Pt/Ni bilayers we find the largest spin polarization in Pt/Fe and a much smaller magnetic proximity effect in Pt/Ni. Additional XRMR experiments with varying photon energy are in good agreement with the theoretical predictions for the energy dependence of the magneto-optical parameters and allow identifying the optical dispersion $\ensuremath{\delta}$ and absorption $\ensuremath{\beta}$ across the $\mathrm{Pt}\phantom{\rule{0.28em}{0ex}}{\mathrm{L}}_{3}$-absorption edge.