Disclosed are (1) a polarizer having a function of separating incident light into polarized light through reflection and transmission, which has (a) a haze of 10% or less, or (b) a ratio of parallel transmitted light to incident light of 40 to 60%, (c) a ratio of mirror reflected light to the incident light of 25% or more, (d) a ratio of diffusion reflected light to the incident light of 20% or less or (e) a fraction of mirror reflected light to the whole reflected light of 60% or more; (2) an optical element comprising the polarizer, and a 1/4 wavelength formed by one or two or more retardation layers disposed on at least one side thereof; (3) a lighting device comprising a surface light source, and the polarizer or the optical element disposed thereon; and (4) a liquid crystal display comprising the lighting device and a liquid crystal cell arranged on the light outgoing side thereof, with a polarizing plate intervening therebetween.