A light source having a light pipe and a light generation section. The light pipe includes a two-dimensional sheet of transparent material having a transparent top surface that is substantially parallel to a reflective bottom surface. The light pipe includes light pipe scattering centers that cause light traveling in the sheet of transparent material to be scattered in directions that allow some of the scattered light to escape the sheet through the top surface. The light generating section includes a plurality of LEDs and a mixing chamber. The LEDs are positioned to emit light into the mixing chamber. The mixing chamber includes an adapter having a wedge-shaped cavity with reflective walls. The cavity has an opening positioned to direct light into the light pipe. The mixing chamber includes scattering centers for redirecting light traveling in the cavity in directions that would not be obtained by reflection from the reflective walls.