Determining size-resolved chemical composition of aerosols is important for modelling the aerosols' direct and indirect climate impact, for source-receptor modelling, and for understanding adverse health effects of particulate pollutants. Obtaining this kind of information from optical remote sensing observations is an ill-posed inverse problem. It can be solved by variational data assimilation in conjunction with an aerosol transport model. One important question is how much information about the particles' physical and chemical properties is contained in the observations. We perform a numerical experiment to test the observability of size-dependent aerosol composition by remote sensing observations. An aerosol transport model is employed to produce a reference and a perturbed aerosol field. The perturbed field is taken as a proxy for a background estimate subject to uncertainties. The reference result represents the 'true' state of the system. Optical properties are computed from the reference results and are assimilated into the perturbed model. The assimilation results reveal that inverse modelling of optical observations significantly improves the background estimate. However, the optical observations alone do not contain sufficient information for producing a faithful retrieval of the size-resolved aerosol composition. The total mass mixing ratios, on the other hand, are retrieved with remarkable accuracy.