In this paper we apply the method of electrical impedance tomography to the problem of determining the interface between two fluid layers in a shallow electrolytic cell. We show that any nontrivial set of boundary currents and corresponding boundary voltages suffices to uniquely identify the interface. We propose a very simple reconstruction method that in an essential way uses the fact that the cell is of very small height. Estimates of the accuracy of this method are also provided. Finally we perform a number of computational experiments to demonstrate the efficiency of the method we propose. For the numerical reconstructions we use synthetic data generated from a discretized boundary integral formulation of the underlying conductivity problem.