  The spontaneous emission of atoms can be controlled by placing them between
two mirrors that form an optical cavity. Rapid advances in material processing
techniques in the last 10 years have made it possible to fabricate microscopic
optical cavities that can be finely tuned into resonance with the emitter. This
has enabled progress in single-photon sources, nano-lasers and spectroscopy of
new nano-emitters such as semiconductor quantum dots and Nitrogen-vacancy
centres in diamond. Here we introduce a step-by-step method for computing the
Purcell factor of the latest generation of open tunable Fabry-Perot
microcavities used in micro-photoluminescence studies. We discuss how the
Purcell factor can be optimised as a function of the cavity's geometry and find
the conditions for resonance with the emitter. Subtleties such as the optical
properties of the emitter and penetration depth of the electric field into the
cavity mirrors are also considered.
