Electromagnetic boundary condition

For linear isotropic media with no free sheet current, continuity of normal $B$ and tangential $H$ gives $\tan {\theta }_2/\tan {\theta }_1={\mu }_2/{\mu }_1$, where the angles are measured from the normal. It is a consequence of the two different magnetic boundary conditions, not continuity of every component of $B$.

With interface normal from medium 1 to medium 2, Ampère's boundary condition is $\hat{\mathbf{n}}\times ({\mathbf{H}}_2-{\mathbf{H}}_1)={\mathbf{K}}_f$. With no free surface current, tangential $H$ is continuous. Normal $B$ is continuous independently because magnetic monopoles are absent.