 Interface conditions for electromagnetic fields

Across an interface with unit normal $\mathbf{n}$ from medium one to medium two, Maxwell equations imply $\mathbf{n}\times ({\mathbf{E}}_2-{\mathbf{E}}_1)=0$, $\mathbf{n}\cdot ({\mathbf{B}}_2-{\mathbf{B}}_1)=0$, $\mathbf{n}\cdot ({\mathbf{D}}_2-{\mathbf{D}}_1)={\sigma }_f$, and $\mathbf{n}\times ({\mathbf{H}}_2-{\mathbf{H}}_1)={\mathbf{K}}_f$. Here ${\sigma }_f$ and ${\mathbf{K}}_f$ are the free surface electric charge and electric current densities.