Context. Asymptotic giant branch (AGB) stars are characterized by substantial mass loss, however the mechanism behind it not yet fully understood. The knowledge of the structure and dynamics of AGB-star atmospheres is crucial to better understanding the mass loss. The recently established tomographic method, which relies on the design of spectral masks containing lines that form in given ranges of optical depths in the stellar atmosphere, is an ideal technique for this purpose. Aims. We aim to validate the capability of the tomographic method in probing different geometrical depths in the stellar atmosphere and recovering the relation between optical and geometrical depth scales. Methods. We applied the tomographic method to high-resolution spectro-interferometric VLTI/AMBER observations of the Mira-type AGB star S Ori. The interferometric visibilities were extracted at wavelengths contributing to the tomographic masks and fitted to those computed from a uniform disk model. This allows us to measure the geometrical extent of the atmospheric layer probed by the corresponding mask. We then compared the observed atmospheric extension with others measured from available 1D pulsation CODEX models and 3D radiative-hydrodynamics CO5BOLD simulations. Results. While the average optical depths probed by the tomographic masks in S Ori decrease (with ⟨log τ₀⟩ = −0.45, − 1.45, and − 2.45 from the innermost to the central and outermost layers), the angular diameters of these layers increase, from 10.59 ± 0.09 mas through 11.84 ± 0.17 mas, up to 14.08 ± 0.15 mas. A similar behavior is observed when the tomographic method is applied to 1D and 3D dynamical models. Conclusions. This study derives, for the first time, a quantitative relation between optical and geometrical depth scales when applied to the Mira star S Ori, or to 1D and 3D dynamical models. In the context of Mira-type stars, knowledge of the link between the optical and geometrical depths opens the way to deriving the shock-wave propagation velocity, which cannot be directly observed in these stars.