Alternative equations of magnetophotoelasticity and approximate solution of the inverse problem

In magnetophotoelasticity, photoelastic models are investigated in a magnetic field in order to initiate rotation of the plane of polarization that is due to the Faraday effect. The method has been used for the measurement of stress distributions that are in equilibrium on the wave normal and therefore cannot be measured with the traditional photoelastic technique. In this category belong bending stresses in plates and shells and residual stresses in glass plates. Two new systems of equations of magnetophotoelasticity are derived. One of them describes evolution of the polarization of light in a magnetophotoelastic medium in terms of eigenvectors, the other in terms of distinctive parameters. For the latter system, an approximate closed-form solution has been found. The integral Wertheim law has been generalized for the case of stress states in equilibrium when rotation of the plane of polarization is present.