Provided are an interactive display apparatus and method for operating an interactive display apparatus, the apparatus including: a capturing unit operable to capture an image including a displayed image which is displayed on a display screen and a light of a pointing device irradiated onto the display screen; a memory which stores the captured image; a detection unit which determines coordinate information for the light of the pointing device irradiated onto the display screen based on the captured image; and a controller which determines whether the light of the pointing device is moved outside of the displayed image based on the coordinate information, and controls the apparatus to perform a predetermined operation from among a plurality of predetermined operations if the light of the pointing device is moved outside of the displayed image.