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We determine the optical constants of non-stoichiometric amorphous magnesium-iron silicates and demonstrate that they can well reproduce the observed mid-infrared emission spectra of evolved stars. Stoichiometric and non-stoichiometric amorphous magnesium-iron silicate films are fabricated by pulsed laser deposition. Transmittance and ellipsometry measurements are performed in the wavelength range between 2 and 200 μm and 1.7 and 33 μm, respectively. Optical constants are derived from transmittance and ellipsometric Ψ and Δ spectra by means of oscillator models. These newly obtained optical constants are applied in radiative transfer models for examining reproducibility of the observed spectral features of circumstellar dust shells around supergiants. The spectra of four selected supergiants are dominated by amorphous silicate dust emission in the wavelength range between 9 and 25 μm. To obtain a good fit to the observed spectra, we take into account amorphous corundum and metallic iron particles as additional dust components to the model calculations to rationalize the dust emission at λ < 8 μm. For each of the objects, a set of model parameters (dust mass and condensation temperature) is derived by an automated optimization procedure that reproduces the observation well. Consequently, our model spectra using new optical data reveal that the silicate bands at ~10 and ~18 μm depend on the magnesium and iron ratio in the silicate system, and that a good fit requires a significant iron content of the amorphous silicate dust component to reproduce the observed peak positions and shape of the silicate bands.