In this work we report on a unique and ancient type of eye, in which the lower surface of the upper calcite lens units possessed an enigmatic central bulge making the dioptric apparatus similar to a bifocal lens. This eye belonged to the trilobite Dalmanitina socialis, which became extinct several hundred million years ago. As far as we know, image formation by bifocal lenses of this kind did/does not occur in any other ancient or modern animal visual system. We suggest that the function of these bifocal lenses may be to enable the trilobite to see simultaneously both very near (e.g. floating food particles and tiny preys) and far (e.g. sea floor, conspecifics, or approaching enemies) in the optical environment through the central and peripheral lens region, respectively. This was the only reasonable function we could find to explain the puzzling lens shape. We admit that it is not clear whether bifocality was necessary for the animal studied. We show that the misleading and accidental resemblance of an erroneous correcting lens surface (designed by René DesCartes in 1637 [DesCartes, R. (1637). Oeuvres de DesCartes. La Géometrie. Livre 2. pp. 134. J. Maire, Leyden] to the correcting interface in the compound Dalmanitina lens may be the reason why the earlier students of the Dalmanitina lens did not recognize its possible bifocality.