The present invention relates to a lighting system comprising a plurality of LEDs emitting light with different colors. The LEDs are provided with collimating optical components (51, 55) in order to emit collimated light beams. The LEDs are arranged in at least two layers (43, 45) and the collimating optical components (51) in the front layer are dichroic reflectors, so that they reflect the light from the associated front layer LED but transmit the light emitted from the rear layer behind. This eliminates or reduces the occurrence of colored edges around shadows on an illuminated surface.