The Verdet constant is the essential parameter of Faraday Effect. Study on Verdet constant of magnetic optical medium is very important in Faraday Effect research and application. In this paper, Verdet constant of liquid and solid medium were investigated with light extinction method with the help of photoelectric detector. Using the square wave magneto-optic modulation method which we established, Verdet constant of air was measured. Variation of Verdet constant of these materials with changes of light wavelength and temperature was investigated. These experimental data may provide reference for research and application of magneto-optic effect. Meanwhile, the experiment in this paper is also one of the key works of magnetic rotation imaging method for geomagnetic field measurement which we proposed. It will provide experimental support for this new geomagnetic field measurement method.