A projection apparatus is specified, comprising a light modulator having a light receiving region with a cross-sectional area to be illuminated of the size AM and a maximum acceptance angle α for incident light, and at least one light source by means of which, during its operation, a light cone is produced for illuminating said cross-sectional area of said light receiving region and which comprises a number N of LED chips having a maximum radiation angle β. At least one of the LED chips has a radiation decoupling area of the size AD. The relation 0.7·(AM·sin2(α))/(AD·sin2(β)·n2)≦N≦1.3·(AM·sin2(α))/(AD·sin2(β)·n2) applies, where n is equal to 1 or to the refractive index of a coupling medium with which the LED chips are provided.