Magneto-optic and electro-optic effects in electromagnetic and gravitational fields

The magneto-optic effects and electro-optic effects are the essential optic effects, although their theoretical explanations are not unified in the classical electromagnetic theory. Describing with the algebra of octonions, the electromagnetic theory can derive the magneto-optic effects and electro-optic effects from the same one force definition in the paper. As well as the magneto-optic effect is deduced from the known force term, the electro-optic effect is from the new force term in the octonion space. This description method is different to that in the quantum theory as well as the index ellipsoid approach for the electro-optic effect. One more significant inference is that the gravitational field has an impact on the rotation of linearly polarized light, and then results in the similar birefringence for the transmitted light in the cosmic matter.