  We measure the coexistence curve and the critical point properties of a
binary mixture composed by polymethylmethacrylate (PMMA) at $M_w = 55900$ g/mol
with 3- octanone. This binary mixture which has a demixing transition with an
upper critical solution temperature $T_c$ has indeed interesting properties
which may be useful for several application : a) its correlation length is
larger than that of a liquid-liquid binary mixture, b) it is less viscous than
a polymer blend; c) 3- octanone has an evaporation rate much smaller than other
solvents. The mixture is first characterized by turbidity, to get the demixing
temperature for different volumic fraction of PMMA. The coordinates of the
critical point are obtained: $\phi_c = 12.8\pm0.2$ % and $T_c = 306.5\pm0.1$ K.
The correlation length $\xi$ near the critical point is then measured in a
solution with a 12.8% volumic fraction of PMMA using static light scattering.
Using the fact that PMMA-octanone mixture has scaling exponents compatible with
Ising 3D, we determine more precisely the critical temperature $T_c =
306.58\pm0.04$ K and we find that $\xi \simeq \xi_0 [(T-T_c)/{T_c}]^{-0.63}$
with $\xi_0 = 0.97\pm 0.02$ nm. The discrepancy between this value and that
extrapolated from other measurements based on turbidity is discussed.
