An accurate method to calculate the negative dispersion generated by prism pairs

Based on the principle of diffraction for light transport in prisms, we figured the physical image for light beams passing through a pair of prisms. The mechanism to induce negative dispersion was analyzed and the numerical expression of optical path length was provided. From a series of mathematical equations, we calculate the quantity of negative dispersion, such as the second- and third-order dispersion, induced by prism pairs. Compared with the expressions of Fork et al. (Opt. Lett. 9(5) (1984) 150), our equations can lead to accurate results and reasonably elucidate the implication of dispersion.