  Recent experimental study reveals the optical conductivity of
La$_{1-x}$Ca$_x$MnO$_3$ over a wide range of energy and the occurrence of
spectral weight transfer as the system transforms from paramagnetic insulating
to ferromagnetic metallic phase [Rusydi {\it et al.}, Phys. Rev. B {\bf 78},
125110 (2008)]. We propose a model and calculation within the Dynamical Mean
Field Theory to explain this phenomenon. We find the role of oxygens in
mediating the hopping of electrons between manganeses as the key that
determines the structures of the optical conductivity. In addition, by
parametrizing the hopping integrals through magnetization, our result suggests
a possible scenario that explains the occurrence of spectral weight transfer,
in which the ferromagnatic ordering increases the rate of electron transfer
from O$_{2p}$ orbitals to upper Mn$_{e_g}$ orbitals while simultaneously
decreasing the rate of electron transfer from O$_{2p}$ orbitals to lower
Mn$_{e_g}$orbitals, as temperature is varied across the ferromagnetic
transition. With this scenario, our optical conductivity calculation shows very
good quantitative agreement with the experimental data.
