  The paper studies the inferences of wave equations for electromagnetic fields
when there are gravitational fields at the same time. In the description with
the algebra of octonions, the inferences of wave equations are identical with
that in conventional electromagnetic theory with vector terminology. By means
of the octonion exponential function, we can draw out that the electromagnetic
waves are transverse waves in a vacuum, and rephrase the law of reflection,
Snell's law, Fresnel formula, and total internal reflection etc. The study
claims that the theoretical results of wave equations for electromagnetic
strength keep unchanged in the case for coexistence of gravitational and
electromagnetic fields. Meanwhile the electric and magnetic components of
electromagnetic waves can not be determined simultaneously in electromagnetic
fields.
