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Summary form only given. We present our work on the modified properties of an optical resonator that contains an electromagnetically induced transparency (EIT) medium. Transparency and steep index of refraction are utilized to reduce the linewidth of the cavity. The influence of the relative intensities of the laser fields is studied, and the results are in good agreement with computer simulations. The linewidth of an optical cavity depends on the phase shift accumulated by the light wave during one round trip. A transparent medium with very strong dispersion causes a very rapidly varying phase shift and would have a remarkable effect on the linewidth of the cavity.