The lidar arrangement (1) has a transmitter (3) for linearly polarized radiation (12), a receiver (5) with a first receiving device which measures intensity of the backscattered radiation (15) coinciding approximately with the transmitted radiation cone (12) in a polarization plane of the cone and in a perpendicular polarization plane, wherein the receiver further includes a second receiving device which measures the intensity of backscattered radiation (17) outside the transmitted cone (12), the outer backscattered radiation has the shape of a conical shell which surrounds the backscattered conical shell of the first mentioned backscattered radiation (15) and of the transmitted cone (12); the received separate radiation cones (15 and 17) are split in a polarization analyzing optical element into two mutually perpendicular partial light beams, each consisting of an inner partial beam portion (15a, 15b) and an outer partial beam portion (17a and 17b), the inner and outer partial beam portions are separately detected and the resulting output signals are amplified by an amplification factor which depends on the distance of the lidar from a visibility obstacle, the distance-corrected amplified signals are evaluated in a signal processing unit to distinguish between different kinds of the visibility obstacle, and the evaluated obstacle such as fog, rain, snow or solid obstacle and a distance thereof are indicated on corresponding indicators.