Three-dimensional (3D) refractive index (RI) tomography has recently become an exciting new tool for biological studies. However, its limitation to (1) thin samples resulting from a need of transmissive illumination and (2) small fields of view (typically ∼50µm×50µm) has hindered its utility in broader biomedical applications. In this work, we demonstrate 3D RI tomography with a large field of view in opaque, arbitrarily thick scattering samples (unsuitable for imaging with conventional transmissive tomographic techniques) with a penetration depth of ca. one mean free scattering path length (∼100µm in tissue) using a simple, low-cost microscope system with epi-illumination. This approach leverages a solution to the inverse scattering problem via the general non-paraxial 3D optical transfer function of our quantitative oblique back-illumination microscopy (qOBM) optical system. A theoretical analysis is presented along with simulations and experimental validations using polystyrene beads, and rat and human thick brain tissues. This work has significant implications for the investigation of optically thick, semi-infinite samples in a non-invasive and label-free manner. This unique 3D qOBM approach can extend the utility of 3D RI tomography for translational and clinical medicine.