The necessity of studying the nature of the propagation of the maximum of the laser radiation pattern in the Anderson differential cell is substantiated. A new technique has been developed for conducting these studies, which takes into account all factors when constructing the trajectory of the maximum laser radiation in the cuvette, as well as outside it (up to the sensor of the photodiode line, on which the radiation is recorded). For the first time, an equation was derived to study the change in the nature of the propagation trajectory of the maximum of laser radiation in the Anderson cell, and beyond it, depending on its various parameters, the values of the refractive indices of the reference ns and the liquid medium under study, nm. The results of checking the reliability of the developed equation are presented. For the first time, a 12th degree polynomial was obtained for Anderson's differential cell with respect to the refractive index of the medium under study to obtain an analytical solution of the developed equation. This solution will provide additional information about the physics of the processes under consideration and the relationships between different quantities.