  The optical conductivity $\sigma_{1}(\omega)$ of Eu$_{1-x}$Ca$_{x}$B$_{6}$
has been obtained from reflectivity and ellipsometry measurements for series of
compositions, $0\leq x\leq 1$. The interband part of $\sigma_{1}(\omega) $
shifts continuously to higher frequency as Ca-content $x$ increases. Also the
intraband spectral weight of $\sigma_{1}(\omega)$ decreases rapidly and
essentially vanishes for $x\geq x_{c}=0.35$. These results show that the
valence band and the conduction band of Eu$_{1-x}$Ca$_{x}$B$_{6}$ move away
from each other such that their band overlap decreases with increasing
Ca-substitution. As a result, the electronic state evolves from the
semimetallic structure of EuB$_{6}$ to the insulating CaB$_{6}$ where the two
bands are separated to open a finite gap ($\simeq 0.25$ eV) at the X-point of
the Brillouin zone.
