A directional backlight comprising a directional waveguide and light sources, the directional waveguide comprising: a reflective end that is elongated in a lateral direction; a rear end facing the reflective end; first and second opposed guide surfaces (6,8) extending from laterally extending edges of the reflective end to the rear end for guiding input light along the waveguide towards the reflective end and for guiding light reflected by the reflective end away from the reflective end, the second guide surface being arranged to deflect light reflected from the reflective end through the first guide surface as output light; and side surfaces (322, 324) extending on the sides of the waveguide between the reflective end and the rear end and between the first and second guide surfaces(6, 8), wherein the reflective end comprises first and second facets (327, 329) alternating with each other in the lateral direction, the first facets being reflective and forming reflective facets of a Fresnel reflector having positive optical power in the lateral direction, the second facets forming draft facets of the Fresnel reflector, characterised in that: the light sources include an array of light sources arranged along one of the side surfaces to provide, through that side surface, said input light that is guided along the waveguide towards the reflective end, and the Fresnel reflector has an optical axis that is inclined towards the side surface along which the array of light sources is arranged, in a direction in which the Fresnel reflector deflects input light from the array of light sources into the waveguide, the waveguide being arranged to direct the output light from the light sources into respective optical windows in output directions that are distributed laterally in dependence on the positions of the light sources. a reflective end that is elongated in a lateral direction; a rear end facing the reflective end; first and second opposed guide surfaces (6,8) extending from laterally extending edges of the reflective end to the rear end for guiding input light along the waveguide towards the reflective end and for guiding light reflected by the reflective end away from the reflective end, the second guide surface being arranged to deflect light reflected from the reflective end through the first guide surface as output light; and side surfaces (322, 324) extending on the sides of the waveguide between the reflective end and the rear end and between the first and second guide surfaces(6, 8), wherein the reflective end comprises first and second facets (327, 329) alternating with each other in the lateral direction, the first facets being reflective and forming reflective facets of a Fresnel reflector having positive optical power in the lateral direction, the second facets forming draft facets of the Fresnel reflector, characterised in that: the light sources include an array of light sources arranged along one of the side surfaces to provide, through that side surface, said input light that is guided along the waveguide towards the reflective end, and the Fresnel reflector has an optical axis that is inclined towards the side surface along which the array of light sources is arranged, in a direction in which the Fresnel reflector deflects input light from the array of light sources into the waveguide, the waveguide being arranged to direct the output light from the light sources into respective optical windows in output directions that are distributed laterally in dependence on the positions of the light sources. the light sources include an array of light sources arranged along one of the side surfaces to provide, through that side surface, said input light that is guided along the waveguide towards the reflective end, and the Fresnel reflector has an optical axis that is inclined towards the side surface along which the array of light sources is arranged, in a direction in which the Fresnel reflector deflects input light from the array of light sources into the waveguide, the waveguide being arranged to direct the output light from the light sources into respective optical windows in output directions that are distributed laterally in dependence on the positions of the light sources.