 Refraction from secondary wavelets

Let a plane incident wavefront first meet a flat interface at $A$, and let another point $B$ on that front reach $C$ on the interface after $\Delta t$. Its path has length $BC=v_1\Delta t$. The secondary wavelet from $A$ has radius $AD=v_2\Delta t$ in the second medium; the new wavefront through $C$ is tangent to it at $D$. Right triangles with common hypotenuse $AC$ give $\sin {\theta }_1=BC/AC$ and $\sin {\theta }_2=AD/AC$, where both ray angles are measured from the interface normal. Consequently $\sin {\theta }_1/\sin {\theta }_2=v_1/v_2=n_2/n_1$, which is Snell's law. The construction uses phase velocities in homogeneous isotropic media.