Ray tracing calculations for crystal-diffraction spectrometers with position-sensitive detectors are done. After describing fundamentals of the ray tracing formalism, the paper presents selected results for a given spectrometer geometry. The developed method allows a three-dimensional representation of diffraction reflections as well as a matrix display of the recorded events in the detector plane. Applying the formalism of Monte Carlo simulation it is possible to calculate other important quantities, such as the resolving power and luminosity of the analyzed spectrometer.