 Method of images

The method of images solves a linear boundary problem by replacing a boundary with fictitious sources chosen so their combined field obeys its conditions. The constructed solution is then justified by a uniqueness of Poisson equation, not by treating the fictitious sources as physically present.

For a charge $q$ at height $a$ above a grounded conducting plane $z=0$, place an image charge $-q$ at height $-a$. In the upper half-space,is zero on the plane and satisfies the required source equation. Dirichlet uniqueness for the Poisson equation identifies it as the physical potential above the conductor. The construction exploits symmetry; arbitrary boundaries need not have a finite set of image sources.

The Method of Images is a mathematical technique used in electrostatics, fluid dynamics, and other areas of physics to simplify the problem of finding potential fields due to charges or other sources in the presence of boundaries. It leverages the principle of superposition and symmetry to replace complex boundary conditions with simpler ones by introducing fictitious charges (or "image charges") in calculated positions.