1. A designated position detector comprising: a display unit having a display area; a detection object fixed and located outside the display area; and an operation member for executing input operations to the display area via space, wherein the operation member is provided with: an image recognizing means for recognizing images; and a control unit for defining the detection object recognized with the image recognizing means at the time of initial setting as a reference image, detecting the relative positional displacement between the image of the detection object recognized with the image recognizing means when the operation member is moved and the reference image, and thereby obtaining a position data on the display area designated with the operation member based on such displacement.