Optical systems for focused light emission, which can be used as full color-capable pixels in grid assemblies, such as variable message signs and outdoor electronic display boards. The optical systems may include a light source that is a commercially available full-color LED in SMD design having a red, a green, and a blue LED crystal, which may be disposed at an inlet surface of a light-guiding rod having a constant cross-section and a jacket surface made of planes adjacent to each other at sharp edges. The light-guiding rod thereby captures the light substantially completely and completely mixes the different colors and brightnesses efficiently without scattering. The light output of the light-guiding rod lies at the focus of a convergent lens, which focuses the exiting light.