A scanning microscope includes an objective and a scanning element that is adjustable for a time-variable deflection to guide a focused illumination beam across the sample in a scanning movement. A detection beam is guided across sensor elements of an image sensor in a movement which corresponds to the scanning movement of the focused illumination beam. A dispersive element of a predetermined dispersive effect arranged upstream of the image sensor spatially separates different spectral components of the detection beam from one another on the image sensor. A controller detects the time-variable adjustment of the scanning element, assigns the spatially separated spectral components of the detection beam to the sensor elements of the image sensor based on the detected time-variable adjustment, while taking into account the predetermined dispersive effect of the dispersive element, and individually reads out the sensor elements assigned to the spectral components.