A lighting system comprising an array of LEDs, collimators for collimating the light output from the LEDs and a lightguide mounted over the array of collimators. The lightguide comprises an elongate structure having a length direction with one light input end mounted over the collimators, wherein the general shape in cross section perpendicular to the length direction comprises a non-circular arc. The array of LEDs is mounted following a corresponding non-circular arc. Light extraction features are provided for out-coupling light from an outer arcuate surface of the lightguide. The non-circular arc formed by the outer surface of lightguide enables a non-uniform light output distribution to be formed. The shape of the surface can thus be used to control the directional light output.