Graphical synthesis of sign conventions in geometrical optics

At least four sign conventions are used for mirrors and thin lenses in geometrical optics. Two conventions only use the Gauss formula involving object, image and focal distances; the other conventions use an additional Gaussian relation. In this paper we compare the sign conventions according to the Gaussian relations they use for mirrors and thin lenses and introduce a diagram for their graphical synthesis. We also explain the details of the standard convention used in our educational environment. School and university teachers can help students to remember and apply the right sign rules using a single diagram, according to the textbook they use. (paper)