A lens for use with a light emitting source is provided. The lens has a main body with a light-collecting face and a light-emitting face and which defines an optical axis extending through the centers of these two faces. A pocket for receiving light from the light source is defined in the light-collecting face by an inner axially-facing surface surrounded by an inner radially-facing surface. The inner axially-facing surface is concave and has a spherical shape. The inner radially-facing surface has a non-spherical, tapered shape and extends between the axially-facing surface and an open end of the pocket. A light assembly incorporating the lens includes a light-emitting diode.