  We have measured the reflectivity spectra of the iron based superconductor
LiFeAs (Tc = 17.6 K) in the temperature range from 4 to 300 K. In the
superconducting state (T < Tc), the clear opening of the optical absorption gap
was observed below 25 cm-1, indicating an isotropic full gap formation. In the
normal state (T > Tc), the optical conductivity spectra display a typical
metallic behavior with the Drude type spectra at low frequencies, but we found
that the introduction of the two Drude components best fits the data,
indicating the multiband nature of this superconductor. A theoretical analysis
of the low temperature data (T=4K < Tc) also suggests that two superconducting
gaps best fit the data and their values were estimated as {\Delta}1 = 1.59 meV
and {\Delta}2 = 3.15 meV, respectively. Using the Ferrell-Glover-Tinkham (FGT)
sum rule and dielectric function {\epsilon}1({\omega}), the superconducting
plasma frequency ({\omega}ps) is consistently estimated to be 6,665 cm-1,
implying that about 59 % of the free carriers in the normal state condenses
into the SC condensate. To investigate the various interband transition
processes (for {\omega} > 200 cm-1), we have also performed the local-density
approximation (LDA) band calculation and calculated the optical spectra of the
interband transitions. The theoretical results provided a qualitative agreement
with the experimental data below 4000 cm-1
