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We analyze the interaction of plane '+'-polarized gravitational waves with aFabry-Perot cavity in the local Lorentz frame of the cavity input mirroroutside of the range of long-wave approximation with the force of radiationpressure taken into account. The obtained detector response signal isrepresented as a sum of two parts: (i) the phase shift due to displacement ofthe movable mirror under the influence of gravitational wave and the force oflight pressure, and (ii) the phase shift due to direct interaction ofgravitational wave with light wave inside the cavity. We obtain formula for themovable mirror law of motion paying close attention to the phenomena of opticalrigidity, radiative friction and direct coupling of gravitational wave to lightwave. Some issues concerning the detection of high-frequency gravitationalwaves and the role of optical rigidity in it are discussed. We also examine indetail special cases of optical resonance and small detuning from it andcompare our results with the known ones.Comment: 17 pages, 9 figures; corrected references [7,8,34], added 2 new  references (currently [35,36]), added comments on (i) relativistic  corrections, (ii) detector angular pattern, (iii) quantized electromagnetic  field, increased font in figure

Interaction of plane gravitational waves with a Fabry-Perot cavity in the local Lorentz frame