A projector producing an imaginary input plane with high operability is provided. A projector according to an embodiment projects a VUI screen picture onto a desk, and projects a main projection screen picture to a wall. The projector includes a light receiving element. The light receiving element is arranged in a position where light emitted toward the desk (VUI screen picture) and reflected (or scattered) by an object near the desk enters. The projector calculates a position of the object based on light sensing timing by the light receiving element and light scan positions at various points in time. The projector changes a projected screen picture when it determines that object is simultaneously in contact with a plurality of portions of the VUI screen picture and at least one of contact positions moves.