Translations:The wave equation/7/en

Points at which a single ray intersects a set of wavefronts are called corresponding points. Evidently, the separation in time between any two corresponding points on any two sequential wavefronts is identical. In other words, if wavefront S transforms into $S^{'}$ after a time $t^{'}$, the distance between corresponding points on any and all rays will be traversed in that same time $t^{'}$. This obviously will be true even if the wavefronts pass from one homogeneous isotropic medium into another. This simply means that each point on S can be imagined as following the path of a ray to arrive at $S^{'}$ in the same time $t^{'}$. Within a homogeneous isotropic medium, the velocity of propagation is identical in all directions. In such a medium, the spatial separation between two wavefronts, measured along a ray, must be the same everywhere.