Ice mixtures of CO2 and H2O are studied using Fourier transform reflection-absorption infrared (RAIR) spectroscopy. Mixtures are prepared by sequential deposition or co-deposition of the two components from the gas phase onto an Al plate kept at 87 K inside a low-pressure chamber. Two CO2 structures are found in most experiments: a crystalline form similar to pure CO2, which evaporates when warming at 105 K, and a noncrystalline species which remains embedded in amorphous water ice after warming. Significant spectral variations are found depending on the deposition method and the thickness of the solid. Features characteristic of the RAIR technique appear in the spectral regions of the normal modes of the bending and asymmetric stretching CO2 vibrations. Simulations using Fresnel theory and Mie scattering are carried out with acceptable agreement with the experimental spectra of solids of variable thickness, from similar to 1 mu m to the limit of nanoparticles. Theoretical calculations of a pure CO2 crystal are performed. The relaxed geometry of the solid and its vibrational spectrum are determined and compared to the experimental results.