The optical magnetic birefringence (Faraday) technique that can be used to study the anisotropy distributions of the angular momenta of photofragments produced in molecular photodissociation is compared theoretically and experimentally with the magnetic dichroism technique. The frame independent tensor form of the general expression describing the difference between an initial and a final polarization matrix of a probe light beam passing through the photofragment vapor is presented and analyzed. The procedure of detection of the photofragment electron orientation and alignment angular distributions by Doppler spectroscopy using each of the techniques is studied theoretically. The angular independent anisotropy orientation and alignment parameters describing photodissociation dynamics that can be determined from these studies are presented. It is shown that in principle each of the techniques can give the same information about the photodissociation dynamics; however, the birefringence technique has an undeniable advantage since it leads to an increase in accuracy of the experimental data. Both magnetic birefringence and magnetic dichroism techniques were used experimentally to study the spin orientation of ground state Rb atoms produced in photodissociation of RbI at 266 nm by circularly polarized laser light. The experiment was not of the Doppler spectroscopy type, but use of different Rb-85 and Rb-87 isotopes in the dissociation cell and in the probe Light source allows detection of the oriented atomic photofragments separately by each of the techniques. Obtained experimental results are in agreement with the theoretical predictions. Contribution of the orientation of the Rb hyperfine structure energy states to the observed signals were also studied and treated theoretically. The initial degree of the electron spin orientation of the Rb atoms produced in the reaction was found to be P-e = 0.11 +/- 0.02.