One of the most widely discussed features of the cuprate high-Tc superconductors is the presence of a pseudogap in the normal state. Recent transport and specific heat measurements have revealed an abrupt transition at the pseudogap critical point, denoted p∗, characterized by a drop in carrier density and a strong mass enhancement. In order to give more details about this transition at p∗, we performed low-temperature infrared spectroscopy in the normal state of cuprate superconductors La2-xSrxCuO4 (LSCO) and La1.8-xEu0.2SrxCuO4 (Eu-LSCO) for doping contents across the pseudogap critical point p∗ (from p = 0.12 to 0.24). Through the complex optical conductivity σ , we can extract the spectral weight K∗ of the narrow Drude peak due the coherent motion of the quasiparticles, and the spectral weight enclosed inside the mid-infrared (MIR) band KMIR caused by coupling of the quasiparticles to collective excitations of the many-body system. K∗ is smaller than a third of the value predicted by band calculations, and KMIR forms a dome as a function of doping. We observe a smooth doping dependence of K∗ through p∗, and demonstrate that this is consistent with the observed doping dependence of the carrier density and the mass enhancement. We argue that the superconducting dome is the result of the confluence of two opposite trends, namely the increase of the density of the quasiparticles and the decrease of their coupling to the collective excitations as a function of doping.