  The behaviour of a "test" electromagnetic field in the background of an exact
gravitational plane wave is investigated in the framework of Einstein's general
relativity. We have expressed the general solution to the de Rham equations as
a Fourier-like integral. In the general case we have reduced the problem to a
set of ordinary differential equations and have explicitly written the solution
in the case of linear polarization of the gravitational wave. We have expressed
our results by means of Fermi Normal Coordinates (FNC), which define the proper
reference frame of the laboratory. Moreover we have provided some "gedanken
experiments", showing that an external gravitational wave induces measurable
effects of non tidal nature via electromagnetic interaction. Consequently it is
not possible to eliminate gravitational effects on electromagnetic field, even
in an arbitrarily small spatial region around an observer freely falling in the
field of a gravitational wave. This is opposite to the case of mechanical
interaction involving measurements of geodesic deviation effects. This
behaviour is not in contrast with the principle of equivalence, which applies
to arbitrarily small region of both space and time.
