An illumination system for producing light and for launching the light into a proximal end of an optical cable of an observation apparatus for endoscopy or microscopy has a light source having at least one LED. In addition, the illumination system has an optical light guiding element between the light source and the proximal end of the optical cable for introducing the light emitted by the light source into the proximal end of the optical cable, wherein a first end region of the optical light guiding element on a side facing the light source has a smaller cross-sectional area than a second end region of the optical light guiding element on a side facing the proximal end of the optical cable. Furthermore, the illumination system has a cooling apparatus which has at least one cooling body and which is thermally conductively connected to the light source in order to remove heat produced by the light source from the illumination system. The cooling body is arranged completely on a side of the light source which is remote from the optical light guiding element.