  From observations of almost 500 RGB stars in 29 Galactic open and globular
clusters, we have investigated the behaviour of the infrared Ca II triplet
(8498, 8542 and 8662 \AA) in the age range 13$\leq$Age/Gyr$\leq$0.25 and the
metallicity range $-2.2\leq$ [Fe/H] $\leq$+0.47. These are the widest ranges of
ages and metallicities in which the behaviour of the Ca II triplet lines has
been investigated in a homogeneous way. We report the first empirical study of
the variation of the CaII triplet lines strength, for given metallicities, with
respect to luminosity. We find that the sequence defined by each cluster in the
Luminosity-$\Sigma$Ca plane is not exactly linear. However, when only stars in
a small magnitude interval are observed, the sequences can be considered as
linear. We have studied the the Ca II triplet lines on three metallicities
scales. While a linear correlation between the reduced equivalent width ($W'_V$
or $W'_I$) versus metallicity is found in the \citet{cg97} and \citet{ki03}
scales, a second order term needs to be added when the \citet{zw84} scale is
adopted. We investigate the role of age from the wide range of ages covered by
our sample. We find that age has a weak influence on the final relationship.
Finally, the relationship derived here is used to estimate the metallicities of
three poorly studied open clusters: Berkeley 39, Trumpler 5 and Collinder 110.
For the latter, the metallicity derived here is the first spectroscopic
estimate available.
