A method and an apparatus for regulating the brightness of a light source (2), configured as an incandescent lamp, in the illumination beam path (8) of a microscope (1), the brightness of the light source (2) being modifiable by increasing or reducing the electrical power delivered to the light source (2), are characterized in that a red shift, associated with the reduction in the delivered electrical power, of the spectrum of the light emitted by the light source (2) in the illumination beam path (8) is compensated for by way of a variable optical filter (16) that brings about a blue shift of the spectrum. A color-neutral regulation of the brightness of the illuminating light is thereby achieved.