A reflective optical element for use in an EUV system is disclosed. The reflective optical element includes a base body, which is produced at least partly from a substrate material. At least one cooling channel through which a cooling medium can flow is arranged in the base body. A material having a thermal conductivity of greater than 50 W/mK is provided as substrate material. The reflective optical element also includes a polishing layer, which is applied on the substrate material. The polishing layer includes an amorphous material which can be processed via polishing.