Mathematics

Problem

Show that if

\mathbf{s}

is a unit vector along the incident ray and

\hat{\mathbf{n}}

is the unit normal to the reflecting plane, then the unit vector

\mathbf{r}

along the reflected ray is given by

\mathbf{r}=\mathbf{s}-2(\mathbf{s}\!\cdot\!\hat{\mathbf{n}})\,\hat{\mathbf{n}}