In this paper we present the Johnson-Cousins UBVR CCD photometry of the stars in King 2, an old open cluster towards the galactic anticenter. We have obtained the colour- magnitude diagram, the colour excess, the reddening, an estimate of the metallicity, and the distance modulus. The comparison of the observational colour- magnitude diagram with the theoretical simulations based on stellar models with convective overshoot shows that a major revision of the model structure is required. To this aim, we explore the possibility that the formulation of convective overshoot for stars in the mass range 1 to 2Msun ought to be different from the one currently in use. The point of major uncertainty that we see to affect the stars in this domain is whether or not convective overshoot may erode the gradient in molecular weight in the regions surrounding the convective core. We find that models, in which this is not allowed to occur, better fit the overall morphology of the colour- magnitude diagram of King 2. In addition to this, analyzing the width of the main sequence band we suggest that a significant fraction of the stars are members of binary systems, and evaluate the range spanned by their mass ratios. Finally, we derive the luminosity function and the mass function for the main sequence stars of the cluster.