When dealing with the topic of finite conjugate, point-source resolution in elementary discussions, we generally take one of two courses. Either we adopt the (somewhat unmotivated) standard Jenkins and White approach or else we try to derive the result on the basis of standard diffraction theory using the known result for the diffraction by a circular aperture. However, the Jenkins and White approach, while giving a believable resolution formula, implies a magnification formula which appears to be wrong. On the other hand, the diffraction approach gives the “correct” magnification formula but its resolution formula implies that infinite resolution is possible for finite wavelength light since the diffraction angle goes to zero for large apertures. It is shown that the key to a coherent presentation of this topic and the resolution of these difficulties is provided by the relatively obscure Abbe's sine theorem.