A detailed investigation of the optical properties of a spherical quantum dot (QD) containing one and two electrons has been performed for cases with and without a hydrogenic impurity. First, the photoionization cross section of both D(0) and D(-) impurities in the QD has been calculated for an on-center impurity. Second, the intersublevel optical absorption and oscillator strength between the ground and excited states have been examined based on the computed energies and wave functions. The full numeric matrix diagonalization technique has been employed in determining sublevel energy eigenvalues and their wave functions. The Poisson-Schrodinger equations have been solved self-consistently in the Hartree approximation. In addition, quantum-mechanical many-body effects have been investigated in the local density approximation. The results are presented as a function of quantum dot radii and photon energies.