1. A stereoscopic image display apparatus comprising: a two-dimensional display device having a display surface formed of a plurality of pixels arranged in a matrix form; and an optical plate which is provided in front of the display surface of the two-dimensional display device, which comprises a plurality of lenses arranged so as to be respectively associated with elemental images each including a plurality of pixels, and which controls light rays illuminated from the pixels, wherein when at least two and less than three elemental images are illuminated in one parallax direction in case where a position of a part or whole of a stereoscopic image is located on a side nearer a viewer than a position indicating a near-side limit value Zno or on a side farther from the viewer than a position indicating a far-side limit value Zfo, the two-dimensional display device displays black in an elemental image of one parallax in elemental images of every two parallaxes.