The diffraction grating experiment revisited

Many A-level and first-year university courses in Physics include an experiment in which the wavelengths of the emission lines of a discharge lamp are measured using a diffraction grating mounted on a standard student spectrometer. The accuracy obtained in practice is usually disappointing as the groove spacing is not accurately known. Therefore a common approach in laboratory courses is to use the wavelength of a known line to calibrate the groove spacing in the grating. Any error in this preliminary measurement, however, is propagated as a systematic error to subsequent measurements. A more instructive approach to the analysis of the data available in this experiment, involving a consideration of both random and systematic error, is outlined.