Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 3 / 14A / b / ii / Solution

Reflect the source point ${\mathbf{r}}_0=(x_0,y_0,z_0)$ across the plane to ${\mathbf{r}}_0^{\ast }=(x_0,y_0,-z_0)$. Equal-sign source and image make the normal derivatives cancel on the plane. Thus the method of images gives the Neumann Green function