 Magnetic field-line refraction at a permeability interface

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 $B$.