Method for controlling display device including transparent screen, and display device therefor

A method of controlling a display device is provided. The method includes a transparent screen to recognize a position of a user in front of the transparent screen and an eye gaze of the user looking at the transparent screen, recognize a position of a background object behind the transparent screen, estimate, based on a distance between the transparent screen and the user, and a direction of the eye gaze of the user, a minimum angular change of the eye gaze by which the display device is able to detect a change in the eye gaze, and display, on the transparent screen, information related to the background object when the background object is at a position within the minimum angular change of the eye gaze from a current eye gaze of the user.