Optical element for forgery proof

An optical element for forgery proof comprising a first layer and a second layer, the optical element being divided into at least a first region and a second region, wherein,

• the first layer is arranged on the second layer having a relief structure on a surface thereof, and the first layer and the second layer have mutually different refractive indexes,
• electromagnetic waves incident at a preset specific angle from a side of the first layer are totally reflected due to at least one of the relief structure in the first region and a ratio of the refractive index of the second layer with respect to the refractive index of the first layer,
• the electromagnetic waves incident at the specific angle from the side of the first layer are not totally reflected but transmitted or refracted due to at least one of the relief structure in the second region and the ratio of the refractive index of the second layer with respect to the refractive index of the first layer,
• wherein when observed from a direction perpendicular to a plane of the optical element, at least one of the first region and the second region generates a parallax image by a convergence angle defined by positions of both eyes and the optical element, and
• wherein
• the second layer has the lower refractive index than the first layer, and the relief structure has an oblique surface tilted with respect to the plane of the optical element, and
• upon observation performed from a given observation point with a light source placed on an observation point side, Formulae 1 and 2 are satisfied:
• θf1≥arcsin(N2/N1) (Formula 1)
• arcsin(N4/N3)>θf2 (Formula 2)
• where
• θf1 denotes an incidence angle on the oblique surface of the relief structure in the first region,
• θf2 denotes an incidence angle on the oblique surface of the relief structure in the second region,
• N1 denotes the refractive index of the first layer in the first region,
• N2 denotes the refractive index of the second layer in the first region,
• N3 denotes the refractive index of the first layer in the second region, and
• N4 denotes the refractive index of the second layer in the second region.