  We study magnetic and critical properties of the alternating spin
antiferromagnetic Heisenberg chain with $S=1/2$ and 1 in a magnetic field at
T=0. The numerical diagonalization is applied to the system up to $2N=20$
sites. Checking numerically that magnetic states with the magnetization per
site $m$ obey a conformal field theory with conformal anomaly $c=1$ for
$1/4<m<3/4$, we use the finite-size scaling of the conformal invariance to
obtain a magentization curve in the thermodynamic limit. In the magnetizatin
curve a plateau appears at $m=1/4$. We also calculate two critical exponents
$\eta$ and $\eta^z$ for $1/4<m<3/4$, which control the asymptotic behavior of
the transverse and parallel spin correlation functions. We check the relation
$\eta \eta^z=1$, which universally holds for a $c=1$ conformal field theory.
