# Translations:Snell’s law/3/en

Ray vector AB in layer 1 has length ${\displaystyle n_{\rm {1}}}$ and makes angle ${\displaystyle {\theta }_{\rm {1}}}$ with the vertical. Ray vector BC in layer 2 has length ${\displaystyle n_{\rm {2}}}$ and makes angle ${\displaystyle {\theta }_{\rm {2}}}$ with the vertical. By Snell’s law, we have ${\displaystyle n_{1}\mathrm {sin} {\theta }_{\rm {l}}{\rm {=}}n_{\rm {2}}{\rm {\ sin\ }}{\theta }_{\rm {2}}}$. This equation says that the horizontal projections of the two ray vectors are the same. We expect this result because the slowness does not change in the horizontal direction. The slowness does E change at the interface in the vertical direction. The shallow medium has slowness ${\displaystyle n_{\rm {l}}}$, and the deep medium has a smaller slowness ${\displaystyle n_{\rm {2}}}$. Because the interface is level, it follows that slowness is constant along any horizontal line, so ${\displaystyle \partial n/\partial x{\rm {=0}}}$. However, slowness does change at the interface. The difference of the slowness at the interface is ${\displaystyle n_{\rm {2}}-n_{\rm {1}}}$, which is negative because ${\displaystyle n_{\rm {2}}{\rm {<}}n_{\rm {1}}}$. The gradient of slowness at the interface is proportional to ${\displaystyle \left(n_{\rm {2}}-n_{\rm {l}}\right)\mathbf {j} }$. This vector points straight into the low-velocity layer. The difference vector BD = BCAB must be proportional to the gradient of the slowness, and hence vector BD must point straight down. Thus, ${\displaystyle n_{\rm {1}}{\rm {\ cos\ }}{\theta }_{\rm {l}}{\rm {>}}n_{\rm {2}}{\rm {\ cos\ }}{\theta }_{\rm {2}}}$, which says that the raypath bends to the right at the interface. In this section, we have given a preview of the ray equation.