= Solution
The <method of images> replaces a conductor's induced <surface charge> by suitable fictitious <image charges> located outside the physical region in which the <electric field> is sought. Choose them so that the combined <electric potential> satisfies the specified conductor boundary values, has the required behaviour at infinity, and has the correct physical sources. The <uniqueness theorem for the electrostatic potential> then identifies this constructed <electric potential> with the physical solution in that region.
For an infinite grounded <conducting plane> at $z=0$, a <point charge> $q$ at $(x,y,z)$ with $z>0$ has an <image charge> $-q$ at $(x,y,-z)$. Distances to the pair are equal on the plane, so their <electric potentials> cancel there. This construction determines the <electric field> above the plane; below it the actual conductor has constant <electric potential> and zero <electric field>, rather than the fictitious image's continuation.
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