By convex lens, rays fallen would be definitely converged hence named as converging lens. If rays fall parallel to the principal axis after refraction they would be converged at a point known to be the principal focus of the lens. If rays go in diverging state as the source is in between its F and O, optic centre then they would appear to come from the same side and so we get a virtual enlarged image. This is what a palmologist does with a lens to read the lines on the palm. Optic centre is the point on the lens through which as rays pass then it goes unrefracted or undeviated.
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They diverge, as in they spread out in straight lines as opposed to coming together like in a magnifying (convex) lens.