  Electrostatic interactions between point charges embedded into interfaces
separating dielectric media are omnipresent in soft matter systems and often
control their stability. Such interactions are typically complicated and do not
resemble their bulk counterparts. For instance, the electrostatic potential of
a point charge at an air-water interface falls off as $r^{-3}$, where $r$ is
the distance from the charge, exhibiting a dipolar behaviour. This behaviour is
often assumed to be generic, and is widely referred to when interpreting
experimental results. Here we explicitly calculate the in-plane potential of a
point charge at an interface between two electrolyte solutions with different
dielectric permittivities and Debye screening lengths. We show that the
asymptotic behaviour of this potential is neither a dipole, which characterises
the potential at air-water interfaces, nor a screened monopole, which describes
the bulk behaviour in a single electrolyte solution. By considering the same
problem in arbitrary dimensions, we find that the physics behind this
difference can be traced to the asymmetric propagation of the interaction in
the two media. Our results are relevant, for instance, to understand the
physics of charged colloidal particles trapped at oil-water interfaces.
