  Temperature dependences of the optical spectra of La$_{2-x}$Sr$_x$CuO$_4$
with $x$=0.12 and 0.15 were carefully examined for a polarization parallel to
the CuO$_2$-plane over a wide frequency range down to 8 cm$^{-1}$. Selection of
well-characterized crystals enabled us to measure purely in-plane polarized
spectra without any additional peak. The weight of superconducting (SC)
condensate estimated from the missing area in $\sigma_1(\omega$) well agrees
with the estimate from the slope of $\sigma_2(\omega$) vs 1/$\omega$ plot,
showing no evidence that the Ferrell-Glover-Tinkham sum-rule is violated in the
optical spectrum. We demonstrate that the optically estimated SC condensate is
much smaller than the value obtained from the $\mu$SR measurement of magnetic
penetration depth. We also find an anomalous increase of conductivity in
sub-millimeter region towards $\omega$=0 below $T_c$, which suggests the
microscopic inhomogeneity in the superconducting state. Both observations are
discussed in relation with the inhomogeneous electronic state that might be
inherent to high-$T_c$ cuprates.
