Ellipsoid-based retrievals are widely used for investigating optical properties of non-ellipsoidal atmospheric particles, such as dust. In this work, the applicability of ellipsoids for retrieving the refractive index of dust-like target model particles from scattering data is investigated. This is a pure modeling study, where stereogrammetrically retrieved model dust shapes are used as targets. The primary objective is to study whether the refractive index of these target particles can be inverted from their scattering matrices using ellipsoidal model particles. To achieve this, first scattering matrices for the target model particles with known refractive indices are computed. On one hand, a non-negative least squares fitting is performed, separately for different scattering matrix elements, for a set of 46 differently shaped ellipsoids by using different assumed refractive indices. Then, the fitting error is evaluated to establish whether the ellipsoidal base best matches the target scattering matrix elements when the correct refractive index is assumed. On the other hand, we also test whether the ellipsoids best match the target data with the correct refractive index, if a predefined (uniform) shape distribution for ellipsoids is assumed, instead of optimizing the shape distribution separately for each tested refractive index. The results show that for both of these approaches using the ellipsoids with the true refractive index produces good results, but also that for each element even better results are acquired by using wrong refractive indices. In addition, the best agreement is found for different scattering matrix elements using different refractive indices. The findings imply that the inversion of refractive index of non-ellipsoidal particles may not be reliable using ellipsoids. Furthermore, it is demonstrated that the differences in single-scattering albedo and asymmetry parameter between the best-match ellipsoid ensemble and the target particles may give rise to major differences in simulated aerosol radiative effects.