This thesis describes an experiment which studies a cloud of magneto-optically trapped potassium-39 atoms inside an optical ring cavity. The potassium atoms are firstly cooled in a two-dimensional magneto-optical trap (MOT) and are then transferred into a three dimensional MOT which overlaps with the cavity mode. In this thesis, the optimisation of the MOT systems and the characterisation and construction of the optical ring cavity are discussed. After exploring these two systems independently, the two systems are then coupled together to provide an atom-cavity system, which exhibits collective strong coupling. The system is shown to exhibit normal-mode splitting, with a collective Rabi splitting of G = 2π (6.25±0.50)MHz, corresponding to (4.7±0.6) x 103 atoms in the cavity. Whilst collective strong coupling has been achieved before in other experiments, we believe this is the first experiment to achieve this with potassium. The next goal in the experiment is to control the group refractive index of the atoms inside the cavity. The modification of the group index using electromagnetically-induced transparency (EIT) on hot atoms inside a vapour cell has already been previously demonstrated by this experiment; and using the same laser system we aim to demonstrate EIT on the cold intra-cavity atoms as well. Gain mechanisms could also be used to create a ring laser with a controllable group index. These techniques could lead to a range of applications such as enhanced-sensitivity laser ring gyroscopes and active optical clocks.