Properties of the optical reference geometry related to Kerr-Newman black-hole and naked-singularity spacetimes are illustrated using embedding diagrams of their equatorial plane. It is shown that among all inertial forces defined within the framework of the optical geometry, just the centrifugal force plays a fundamental role in connection with the embedding diagrams because it changes sign at the turning points of the diagrams. The embedding diagrams do not cover the stationary part of the Kerr-Newman spacetimes completely. Hence, the limits of embeddability are given, and it is established which of the photon circular orbits hosted by the Kerr-Newman spacetimes appear in the embeddable regions. Some typical embedding diagrams are constructed, and the Kerr-Newman backgrounds are classified according to the number of embeddable regions of the optical geometry as well as the number of their turning points. It is shown that embedding diagrams are closely related to the notion of the radius of gyration which is useful for analysing a fluid rotating in strong gravitational fields.