= Solution
The <method of images> replaces <electrical conductors> by fictitious <image charges> outside the physical region. Choose the <image charges> so that the physical <electric charges> and their images produce the prescribed constant <electric potential> on every conducting boundary. The <uniqueness theorem for the electrostatic potential> then identifies this constructed <electric potential> with the physical solution in the charge-containing region. Several conducting planes can require several, or infinitely many, <image charges>; a single reflected image is sufficient for one infinite plane.
Put the plane at $z=0$ and the <point charge> at $(0,0,d)$. For $z>0$, use an <image charge> $-q$ at $(0,0,-d)$:
$$
\phi(x,y,z)=\frac{q}{4\pi\epsilon_0}\left[\frac1{\sqrt{x^2+y^2+(z-d)^2}}-\frac1{\sqrt{x^2+y^2+(z+d)^2}}\right].
$$
This vanishes on the plane. An arbitrary constant can be added if a different reference <electric potential> is chosen. Excluding the <point charge>'s own <electric field>, <Coulomb's law> gives
$$
\boxed{\mathbf F=-\frac{q^2}{16\pi\epsilon_0d^2}\,\hat{\mathbf z}.}
$$
The separation from the <image charge> is $2d$, and the <force> is attractive for either sign of $q$. No imposed external <electric field> is included.
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