It was shown that the assumption of straight-line probing beams, which is usually used in reconstructing the plasma density profile from interferometric measurements, leads to unacceptably large errors in the case of a dense plasma. A fast method based on the assumptions of geometric optics is proposed for calculating the interferometric signal. This method takes into account the refraction of the probe wave and can be used in reconstruction of the plasma density profile. The method correctness is confirmed by comparison with the results of full-wave calculations.