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The temperature dependence of the $ab$-plane optical reflectivity ofBa(Fe$_{0.92}$Co$_{0.08})_2$As$_{2}$ and Ba(Fe$_{0.95}$Ni$_{0.05})_2$As$_{2}$single crystals is measured in a wide spectral range. Upon entering thesuperconducting regime, the reflectivity in both compounds increasesconsiderably at low frequency, leading to a clear gap in the opticalconductivity below 100 cm$^{-1}$. From the analysis of the complex conductivityspectra we obtain the penetration depth $\lambda(T)=(3500\pm 350)$ \AA forBa(Fe$_{0.92}$Co$_{0.08})_2$As$_{2}$ and $(3000\pm 300)$ \AA forBa(Fe$_{0.95}$Ni$_{0.05})_2$As$_{2}$. The calculated superfluid density$\rho_s$ of both compounds nicely fits the scaling relation $\rho_s=(125\pm25)\sigma_{dc}T_c$.

Superfluid density of Ba(Fe$_{1-x}M_x$)$_2$As$_2$ from optical experiments