A directional backlight apparatus comprising: a waveguide extending between an input end for receiving input light and a reflective end for reflecting the input light back through the waveguide; an array of light sources disposed at different input positions in a lateral direction across the input end of the waveguide, the waveguide having first and second, opposed guide surfaces (6, 8) extending between the input end and the reflective end for guiding light forwards and back along the waveguide, the waveguide being arranged to reflect input light from light sources at the different input positions across the input end after reflection from the reflective end into respective optical windows in output directions distributed in the lateral direction in dependence on the input positions; and a control system (75, 76) arranged to selectively operate the light sources to direct light into a selectable viewing windows, wherein the reflective end converges the reflected light such that reflected light from light sources that are offset from the optical axis of the waveguide fails to illuminate outer portions of the waveguide, the waveguide further comprises sides (244, 246), extending between the input end and the reflective end and between the guiding surfaces (6, 8), that are planar surfaces arranged to reflect light from the light sources, wherein the sides (244, 246) of the waveguide diverge from the input end to the reflective end, or converge from the input end to the reflective end, and the control system (75, 76) being arranged, on selective operation of a first light source to direct light into a viewing window, to simultaneously operate a second light source that directs light reflected by the reflective end and then by a side (244, 246) of the waveguide into the outer portion of the waveguide that fails to be illuminated by the first light source. a waveguide extending between an input end for receiving input light and a reflective end for reflecting the input light back through the waveguide; an array of light sources disposed at different input positions in a lateral direction across the input end of the waveguide, the waveguide having first and second, opposed guide surfaces (6, 8) extending between the input end and the reflective end for guiding light forwards and back along the waveguide, the waveguide being arranged to reflect input light from light sources at the different input positions across the input end after reflection from the reflective end into respective optical windows in output directions distributed in the lateral direction in dependence on the input positions; and a control system (75, 76) arranged to selectively operate the light sources to direct light into a selectable viewing windows, wherein the reflective end converges the reflected light such that reflected light from light sources that are offset from the optical axis of the waveguide fails to illuminate outer portions of the waveguide, the waveguide further comprises sides (244, 246), extending between the input end and the reflective end and between the guiding surfaces (6, 8), that are planar surfaces arranged to reflect light from the light sources, wherein the sides (244, 246) of the waveguide diverge from the input end to the reflective end, or converge from the input end to the reflective end, and the control system (75, 76) being arranged, on selective operation of a first light source to direct light into a viewing window, to simultaneously operate a second light source that directs light reflected by the reflective end and then by a side (244, 246) of the waveguide into the outer portion of the waveguide that fails to be illuminated by the first light source.