  The dynamics of light in Fabry-Perot cavities with varying length and input
laser frequency are analyzed and the exact condition for resonance is derived.
This dynamic resonance depends on the light transit time in the cavity and the
Doppler effect due to the mirror motions. The response of the cavity to length
variations is very different from its response to laser frequency variations.
If the frequency of these variations is equal to multiples of the cavity free
spectral range, the response to length is maximized while the response to the
laser frequency is zero. Implications of these results for the detection of
gravitational waves using kilometer-scale Fabry-Perot cavities are discussed.
