The heavy-fermion compound CeRhIn₅ can be tuned through a quantum critical point, when In is partially replaced by Sn. In this way additional charge carriers are introduced and the antiferromagnetic order is gradually suppressed to zero temperature. Here we investigate the temperature-dependent optical properties of CeRh(In_1−xSn_x)₅ single crystals for x=4.4%, 6.9%, and 9.8%. With increasing Sn concentration the infrared conductivity reveals a clear enhancement of the c−f hybridization strength. At low temperatures we observe a non-Fermi-liquid behavior in the frequency dependence of the scattering rate and effective mass up to approximately 50 meV in all three compounds. In addition, below a characteristic temperature T^∗ ≈ 10 K, the temperature-dependent resistivity ρ(T) follows a logT behavior, typical for a non-Fermi-liquid. The temperature-dependent magnetization also exhibits anomalous behavior below T^∗. Our investigation reveal that below T^∗ the system shows a pronounced non-Fermi-liquid behavior and T^∗ monotonically increases as the quantum critical point is approached.