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We consider tests of Lorentz invariance for the photon and fermion sectorthat use vacuum and matter-filled cavities. Assumptions on the wave-function ofthe electrons in crystals are eliminated from the underlying theory andaccurate sensitivity coefficients (including some exceptionally large ones) arecalculated for various materials. We derive the Lorentz-violating shift in theindex of refraction n, which leads to additional sensitivity for matter-filledcavities ; and to birefringence in initially isotropic media. Using publishedexperimental data, we obtain improved bounds on Lorentz violation for photonsand electrons at levels of 10^-15 and below. We discuss implications for futureexperiments and propose a new Michelson-Morley type experiment based onbirefringence in matter.Comment: 15 pages, 8 table

Testing Lorentz invariance by the use of vacuum and matter filled cavity resonators