A film having a high transmittance and matt property utilizable for an optical film on a backlight side of a liquid crystal cell in a liquid crystal display device, comprising a transparent support, a hard coat layer and a low refractive index layer having a refractive index lower than that of the transparent support overlaid in the written order, the hard coat layer containing inorganic fine particles having been treated on the surface thereof with a silane-coupling agent, a crosslinked polymeric binder, and monodisperse transparent fine particles having an average particle diameter greater than the thickness of the hard coat layer and a particle diameter distribution of 0.2 or less in terms of a variation coefficient, and the surface roughness Ra being 0.1 to 0.3 μm and Rz being 1 to 3 μm.