A projector (1) for imaging an original image on a projection area (5) includes projection optics (2) having an adjustable image width (L) for imaging the original image on the projection area (5). A camera device (6) is used for imaging the projection area (5) and generating a projection area image. A comparison device (12) compares the original image with the projection area image and adjusts the image width (L) of the projection optics (2) as a function of the comparison such that the comparison device (12) is configured to determine the position of the original image in the projection area image. The position of the original image in the projection area image is then used as a measure for determining the image width of the projection optics (2).