The honeycomb compound alpha-RuCl3 is widely discussed as a proximate Kitaev spin-liquid material. This scenario builds on spin-orbit entangled j = 1/2 moments arising for a t(2g)(5) electron configuration with strong spin-orbit coupling lambda and a large cubic crystal field. The actual low-energy electronic structure of alpha-RuCl3, however, is still puzzling. In particular, infrared absorption features at 0.30, 0.53, and 0.75 eV seem to be at odds with a j = 1/2 scenario. Also the energy of the spin-orbit exciton, the excitation from j = 1/2 to 3/2, and thus the value of lambda, are controversial. Combining infrared and Raman data, we show that the infrared features can be attributed to single, double, and triple spin-orbit excitons. We find lambda = 0.16 eV and Delta = 42(4) meV for the observed noncubic crystal-field splitting, supporting the validity of the j = 1/2 picture for alpha-RuCl3. The unusual strength of the double excitation is related to the underlying hopping interactions, which form the basis for dominant Kitaev exchange.