Cavity ring-down is becoming a widely used technique in gas phase spectroscopy. It holds promise for further important extensions, which will lead to even more frequent use. However, we have found widespread confusion in the literature about the nature of coherence effects, especially when the optical cavity constituting the ring-down cell, is excited with a short coherence length laser source. In this paper we use the superposition principle of optics to present a general and natural framework for describing the excitation of a ring-down cavity regardless of the relative values of the cavity ring-down time, the input pulse coherence time, or the dephasing time of absorption species inside the cavity. This analysis demonstrates that even in the impulsive limit the radiation inside a high finesse cavity can have frequency components only at the natural resonance frequencies of the cavity modes. As an immediate consequence, a sample absorption line can be detected only if it overlaps at least one of the cavity resonances. Since this point is of particular importance for high resolution applications of the technique, we have derived the same conclusion also in the time domain representation. Finally, we have predicted that it is possible to use this effect to do spectroscopy with a resolution much higher than that of the bandwidth of the excitation laser. In order to aid in the design of such experiments, expressions are derived for the temporal and spatial overlap of a Fourier transform Limited input Gaussian beam with the TEM,, modes of the cavity. The expressions we derive for the spatial mode overlap coefficients are of general interest in applications where accurate mode matching to an optical cavity is required.