A sensor assembly having a radiation receiver and a radiation emitter, and a windscreen wiping device are assigned to the window surface of the motor vehicle. The radiation emitter emits a radiation signal to the window surface and reflected on a boundary surface with the environment surrounding the vehicle. A radiation measurement value of the reflected radiation signal is detected by the radiation receiver. When an increased amount of reflected radiation is detected, this indicates a deposit on the window surface, and the windscreen wiping device is initiated to wipe the window surface. A further radiation measurement value of the reflected radiation is detected after wiping with the windscreen wiping device. The radiation measurement value detected after wiping is compared with the radiation measurement value detected before wiping. If the difference between the radiation measurement values before and after wiping is small enough, it indicates dirt on the window surface.