An optical device comprises a transparent plate the first surface of which is reflective; a first partially reflective and partially transmissive layer covering a second surface of the transparent plate opposite the first surface, and a second layer covering the surface of the first layer opposite the transparent plate, wherein the second layer is made of a material having an optical index which differs from the optical index of the transparent plate by less than 10% and preferably by less than 5%, and the second layer comprises, on the surface thereof opposite the first layer, structures forming a diffraction grating suitable for promoting the extraction of light towards the outside of the transparent plate.