An illumination apparatus having a first illumination unit and a second illumination unit is provided. Each illumination unit has an LED arrangement and a supply device. Each LED arrangement has at least one LED group having a multiplicity of LEDs. A control device for driving the at least two illumination units with a common nominal dim drive value is included. The nominal dim drive value drives the illumination units in such a way that the similar LED groups of the illumination units are operated in a dim mode. The apparatus also has an offset device, which is formed to derive an absolute dim drive value for each of the similar LED groups from the nominal dim drive value with an offset value. The offset value is selectively assigned to the LED group and selected, such that the LED group is activated by the absolute dim drive value.