  In pump-probe spectroscopy, one often needs to analyse the transmission or
reflection of electromagnetic waves through optically pumped media. Here, it is
common practice to approximate the analysis in order to extract non-equilibrium
values for the optical constants of the media. Concentrating on optical
pump-THz probe spectroscopy, and using the transfer matrix approach, we present
a general method for evaluating the applicability of the most common
approximations. Somewhat surprisingly, we find that these approximations are
truly valid only in extreme cases where the optical thickness of the sample is
several orders of magnitude smaller or larger than the probe wavelength.
