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Concave lens diverges the light rays because of its surface on each end. The concave shape bends the rays coming on to them away from the principal axis and away from the Pole. So the rays diverge and they do not meet after refraction.

The rays parallel to principal axis bend towards vertical at the first surface and further upwards at the second surface. This happens for the parallel rays above the principal axis. For rays that are incident below the principal axis, the par axial rays diverge away from principal axis and towards down ward direction. So all the rays from the lens diverge.

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