  The derivation of the response function of an interferometric gravitational
wave detector is a paradigmatic calculation in the field of gravitational wave
detection. Surprisingly, the standard derivation of the response wave detectors
makes several unjustifiable assumptions, both conceptual and quantitative,
regarding the coordinate trajectory and coordinate velocity of the null
geodesic the light travels along. These errors, which appear to have remained
unrecognized for at least 35 years, render the "standard" derivation inadequate
and misleading as an archetype calculation. Here we identify the flaws in the
existing derivation and provide, in full detail, a correct derivation of the
response of a single-bounce Michelson interferometer to gravitational waves,
following a procedure that will always yield correct results; compare it to the
"standard", but incorrect, derivation; show where the earlier mistakes were
made; and identify the general conditions under which the "standard" derivation
will yield correct results. By a fortuitous set of circumstances, not generally
so, the final result is the same in the case of Minkowski background spacetime,
synchronous coordinates, transverse-traceless gauge metric perturbations, and
arm mirrors at coordinate rest.
