A formalism to connect first-order Raman intensities of MgF₂ and its photoelastic constants is developed by developing a method of writing internal coordinates in terms of displacement gradientsu_ij which are not symmetric. It is found that for crystals containing only one line inA₁ species, the ratiosP₁₃/P₃₃ and (P₁₁ +P₁₂)/P₃₁ can be directly evaluated from the intensities, without having to derive the intensity formulae; while (P₁₁ +P₁₂)/P₁₃ is independent of the intensities as well as the refractive index of the crystal. It is a function of only the dimensional parameters. In this crystal, since the speciesB_1g andB_2g also contain only one line each, the ratio (P₁₁ −P₁₂)/P₆₆ can also be directly obtained from the intensities.