  We consider the radiative trapping and cooling of a partially transmitting
mirror suspended inside an optical cavity, generalizing the case of a perfectly
reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys.
Rev. Lett. \textbf{99}, 073601 (2007)]. This configuration was recently used in
an experiment to cool a nanometers-thick membrane [Thompson \textit{et al.},
arXiv:0707.1724v2, 2007]. The self-consistent cavity field modes of this system
depend strongly on the position of the middle mirror, leading to important
qualitative differences in the radiation pressure effects: in one case, the
situation is similar that of a perfectly reflecting middle mirror, with only
minor quantitative modifications. In addition, we also identify a range of
mirror positions for which the radiation-mirror coupling becomes purely
dispersive and the back-action effects that usually lead to cooling are absent,
although the mirror can still be optically trapped. The existence of these two
regimes leads us to propose a bichromatic scheme that optimizes the cooling and
trapping of partially transmissive mirrors.
