  The heavy-fermion compound CeRhIn$_5$ can be tuned through a quantum critical
point, when In is partially replaced by Sn. 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$_{1-x}$Sn$_x$)$_5$ 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
observed a non-Fermi-liquid behavior in the frequency dependence of the
scattering rate and effective mass in all three compounds. In addition, below a
characteristic temperature $T^* \approx 10$ K, the temperature dependent
resistivity $\rho(T)$ follows a $\log T$ 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.
