= Solution
The <Huygens-Fresnel principle> treats every point of an advancing <wavefront> as a source of secondary <spherical waves>; their forward envelope constructs the next <wavefront>. Consider two points where an oblique plane <wavefront> meets a plane interface a distance $AB$ apart. After its first point reaches $A$, let time $t$ elapse until the second reaches $B$. In medium 1, the incident travel distance is $v_1t=AB\sin i$. Meanwhile, a secondary <wave> from $A$ has travelled distance $v_2t$ in medium 2. The tangent from $B$ to that secondary <wavefront> gives $v_2t=AB\sin r$. Therefore
$$
\frac{\sin i}{\sin r}=\frac{v_1}{v_2}=\frac{n_2}{n_1},
\qquad\boxed{n_1\sin i=n_2\sin r.}
$$
Here $i,r$ are the <angle of incidence> and <angle of refraction>, measured from the interface <normal vector>, and $n_j=c/v_j$ are the <refractive indices> at the common <frequency>. This is <Snell's law>.
Back to article page
