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We present a theoretical study of the energy spectrum of single electron and hole states in quantum dots of annular geometry under a high magnetic field along the ring axis in the frame of uncorrelated electron-hole theory. We predict the periodic disappearance of the optical emission of the electron-hole pair as the magnetic field increases, as a consequence of the finite height of the barriers. The model has been applied to semiconductor rings of various internal and external radii, giving as limiting cases the disk and antidot. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200673.21.La Quantum dots, 71.35.Ji Excitons in magnetic fields; magnetoexcitons, 73.23.Ra Persistent currents, 78.67.Hc Quantum dots,

Finite size effects on the optical transitions in quantum rings under a magnetic field