The experimental results of the first and second rainbows for water, alcohol jet and fiber are measured by rainbow refractometer with a linear CCD camera. Based on Mie theory the rainbow intensity distribution is calculated, and numerical results agree with the experiment. The limitation of the geometric optics and Airy theory is discussed. And the rainbow phenomena are interpreted reasonably by using geometric optics and Mie theory. The refractive index can be determined by the first rainbow angle. Based on the fast Fourier transform of the derivative distribution of rainbow intensities, the diameter of a droplet is measured by the angular frequencies. The precision of measurement is also discussed by means of the angular frequency.