Abstract: A tapered-waveguide display apparatus includes an input waveguide (2) in the form of a slab, into one end of which light can be injected from a projector (6) so that it bounces along the waveguide and exits at the other end, and a tapered output waveguide (1) adapted to receive light from the input waveguide at its blunt end, that then bounces at ever steeper angles until it reaches the critical angle, at which point it is emitted from the face of the taper. In order to eliminate dark gaps in the display the tapered waveguide's thickness profile is varied so that light bounces the same number of times in total before leaving the tapered waveguide.