  The intensive search for alternative non-cuprate high-transition-temperature
($T_c$) superconductors has taken a positive turn recently with the discovery
of superconductivity in infinite layer nickelates. This discovery is expected
to be the basis for disentangling the puzzle behind the physics of high $T_c$
in oxides. In the unsolved quest for the physical conditions necessary for
inducing superconductivity, we report an optical study of a
Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ film measured using optical spectroscopy, at
temperatures above and below the critical temperature $T_c\sim 13$ K. The
normal-state electrodynamics of Nd$_{0.8}$Sr$_{0.2}$NiO$_2$, is described by
the Drude model characterized by a scattering time just above $T_c$ ($\tau \sim
1.7\times 10^{-14}$ s) and a plasma frequency $\omega_p = 8500$ cm$^{-1}$ in
combination with an absorption band in the Mid-Infrared (MIR) around $\omega_0
\sim 4000$ cm$^{-1}$. The MIR absorption indicates the presence of strong
electronic correlation effect in the NiO$_2$ plane similarly to cuprates. Below
$T_c$, a superconducting energy gap ($2\Delta$) of $\sim 3.2$ meV is extracted
from the Terahertz reflectivity using the the Mattis-Bardeen model. From the
Ferrel-Glover-Thinkam Rule applied to the real part of the optical
conductivity, we also estimate a London penetration depth of about 490 nm, in
agreement with a type-II superconductivity in Nd$_{0.8}$Sr$_{0.2}$NiO$_2$
Nickelate.
