In this paper, the authors write
Matching the optical boundary conditions at the air/graphene/SiC interfaces, the optical transmission $t(\omega)$ through $N$ graphene layers on a SiC wafer (normalized to the transmission through a plain graphene wafer) can be written as $$ t(\omega) = \frac{1}{1+N\sigma(\omega)\sqrt{\mu_{0}/\epsilon_{0}}/(1+n_{\rm{SiC}}) } $$ where $n_{\rm{SiC}}$ is the refractive index of SiC.
In this paper, the same authors write
Matching the optical boundary conditions at the air/graphene/SiC interfaces, the optical transmission $T(\omega)$ through $N$ graphene layers on a SiC wafer (normalized to the transmission through a plain SiC wafer) can be written in terms of the complex optical conductivity $\sigma(\omega)$ as $$ T(\omega) = \left|1 + N\sigma(\omega)\sqrt{\mu_{0}/\epsilon_{0}}/(1+n_{\rm{SiC}}) \right|^{-2} $$
These two expressions do not reduce to each other in the limit $\Im(\sigma(\omega))\to 0$, or in the limit $|\sigma(\omega)| \to 0$. What have I missed that explains this discrepancy?
