A thin plastic light guide is formed to have cavities on one surface and TIR (total internal reflection) structures directly above the cavities. LEDs mounted on a printed circuit board are positioned in the cavities. The cavity walls are shaped to refract the LED light and direct the LED light toward the TIR structures to most efficiently make use of the TIR structures. The TIR structures may have a cusp or cone shape. The top ceiling of the cavities may be shaped to direct light at the TIR structure so as to leak through the TIR structure and blend the light with light leaking through surrounding portions of the light guide. The LEDs may be distributed only near the edges of the light guide or over the entire back surface of the light guide. A diffuser sheet may be laminated over the light guide to further mix the light.