Thermal noise computation in gravitational wave interferometers from first principles

•A new method for computation of thermal noise in solids is proposed.•Readout variable in optomechanical systems is related to the Maxwell stress tensor of moving dielectric surfaces.•The fluctuations of a dielectric media in FP cavity depend on the ratio between the lengths of the cavity and media.•The polarization of light and value of folding angle have impact on the thermal noise of folding mirrors.