= Finite image construction for a planar wedge
{title2=$\arg z\in(0,\pi/N),\quad z_k^+=z_0e^{2\pi ik/N},\quad z_k^-=\overline{z_0}e^{2\pi ik/N}$}
For a positive integer $N$, a point source in a grounded planar wedge of opening $\pi/N$ can be supplemented by $2N-1$ images. Keep positive sources at $z_0e^{2\pi ik/N}$ and negative sources at $\overline{z_0}e^{2\pi ik/N}$, $k=0,\ldots,N-1$, counting the actual source as the first positive one. Reflection in either boundary pairs equal distances with opposite signs, so the logarithmic <electrostatic potential> vanishes on both rays. Every image lies outside the open physical wedge.
The identity $\prod_k(z-z_0e^{2\pi ik/N})=z^N-z_0^N$ compresses the image sum to
$$
\Phi(z)=-\frac e{2\pi\varepsilon_0}\log\left|\frac{z^N-z_0^N}{z^N-\overline{z_0}^{\,N}}\right|.
$$
Here the normalization is that of a two-dimensional point source, equivalently a charge per unit length in a translationally invariant three-dimensional problem. For $N=3$, a source on the bisector with unit radius has $z_0^3=i$, giving the ratio $(z^3-i)/(z^3+i)$. The <method of images> works finitely here because successive boundary reflections generate a finite rotation group; arbitrary wedge angles need not have a finite image construction.
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