The fundamental optical problem encountered in three‐dimensional photoelasticity is that of the propagation of light in a heterogeneous, aeolotropic medium. Although there is an extensive literature on the homogeneous, aeolotropic medium and the heterogeneous, isotropic medium, only a few special cases of the combined problem have been studied from the point of view of Maxwell's electromagnetic equations. With regard to approximate treatments, the most general is that of F. Neumann (1841), derived from purely kinematical considerations. In the present paper the passage from Maxwell's to Neumann's equations is executed and the nature and order of magnitude of the necessary approximations are disclosed. During the passage, there are discovered a pair of equations, of relatively simple form, which open the way to a variety of new solutions in closed form and reveal the essential parameter upon which the optical phenomena depend.