A method, an optical system and a lighting arrangement for homogenizing a bundle of light rays (110) by means of an elongated optical element (100) arranged for homogenizing light. The bundle of light rays is directed into a transversal entry face (101) of the optical element, and into at least one of the following geometrical regions: (a) a neighbourhood of the perimeter of the entry face (b) a neighbourhood of at least a portion of a first line segment (R1) extending from the centre of the entry face to a mid-point of a vertex (123) (c) a neighbourhood of at least a portion of a second line segment (R2a) extending from the centre of the entry face to a midpoint of an edge (122).
