An astronomy laboratory exercise has been developed which allows students to discover for themselves the relationship between the temperature and luminosity changes in Cepheid variable stars. The equipment used is either easily constructed or readily available from among instruments commonly found in physics departments. A sinusoidally varying light source is monitored using a telescope-photomultiplier tube combination. Filters are employed allowing color index information to be obtained. The light curves are recorded on a strip-chart recorder, allowing each student to make his own observations and use his own chart recording in the data reductions.