This invention is an illumination system that incorporates a light emitting diode and a partially reflecting optical element. The light emitting diode emits internally generated light and reflects incident light with high reflectivity. The partially reflecting optical element transmits a first portion of the internally generated light and reflects a second portion of the internally generated light back to the light emitting diode, where the second portion is reflected by the light emitting diode. The partially reflecting optical element can be a non-absorbing reflecting polarizer or a wavelength conversion layer. Utilizing a partially reflecting optical element and light recycling can increase the effective brightness and the output efficiency of the illumination system.