When performing paraxial ray trace calculations, it was usually only necessary to trace the paraxial marginal and chief rays. In real ray tracing, in order to account for aberration, it is necessary to trace a grid of rays through the pupil. As a minimum, 5 real rays must be traced: 1. the axial marginal ray (system marginal ray) 2. the full-field chief ray (system chief ray) 3. the full-field marginal ray at =0 4. the full-field marginal ray at =90 5. the full-field marginal ray at =180 For a system with: Object height: 10mm Object distance: 50mm in front of the 1st optical surface Entrance pupil position: 10mm in front of first lens Entrance pupil diameter: 8mm Determine the starting coordinates and direction cosines of the 5 specified rays