We calculate from first principles the optical spectra of the hydrides in the sodium alanate hydrogen storage system: NaH, NaAlH4, and Na 3AlH6. In particular we study the effects of systematic improvements of the theoretical description. To benchmark the calculations we also measure the optical response of a thin film of NaH. The simplest calculated dielectric functions are based upon independent electrons and holes, whose spectrum is obtained at the G0W0 level. Successive improvements consist of including partial self-consistency (so-called GW 0) and account for excitonic effects, using the Bethe-Salpeter equation (BSE). Each improvement gives a sizable blue shift or red shift of the dielectric functions, but conserves the trend in the optical gap among different materials. Whereas these shifts partially cancel at the highest (GW 0-BSE) level of approximation, the shape of the dielectric functions is strongly modified by excitonic effects. Calculations at the GW 0-BSE level give a good agreement with the dielectric function of NaH extracted from the measurements. It demonstrates that the approach can be used for a quantitative interpretation of spectra in novel hydrogen storage materials obtained via, e.g., hydrogenography.@en