= Solution
<Huygens' principle> treats each point of a <wavefront> as the source of a secondary wavelet. The later <wavefront> is the common forward envelope of those wavelets. Consider a plane front reaching a flat interface between media with speeds $v_1$ and $v_2$. In the same interval $\Delta t$, the incident front advances $v_1\Delta t$ while the first transmitted wavelet grows to radius $v_2\Delta t$.
The two right triangles sharing the interface segment of length $d$ give $d\sin i=v_1\Delta t$ and $d\sin r=v_2\Delta t$, where $i$ and $r$ are ray angles to the normal. Hence
$$
\frac{\sin i}{\sin r}=\frac{v_1}{v_2}=\frac{n_2}{n_1},\qquad\boxed{n_1\sin i=n_2\sin r.}
$$
This is <Snell's law>. The frequency is unchanged at a stationary interface, while wavelength changes with the propagation speed.
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