A computational investigation has been carried out on the design and properties of the electrostatic ion mirrors. The work has been focused on suggesting two mathematical expressions to represent the axial potential of an ion mirror. The functions that have been taken into consideration were those which gave rise to the mirror action. Studying the ion beam path under infinite magnification conditions and study the ion beam path by using the Bimurzaev technique have been investigated as a mirror trajectory with aid of Runge-Kutta method. The electrodes shapes of each mirror have been determined in two and three dimension. In the present work the profile of the mirror that applied under infinite magnification condition determined from the suggested potential is of the three-electrodes. The profile of the mirror that applied by using Bimurzaev technique determined from the suggested potential is of two-electrodes. Both mirrors have an axial bore to provide a passage for the ion beam undergoing a mirror trajectory. The spherical and chromatic aberration coefficients of both mirrors have computed and normalized in terms of the focal length. The choice of the mirror depends on the operational requirements, i.e. whether it is intended to operate the mirror in an ion-optical system at low spherical aberration or low chromatic aberration. Computations have shown that the suggested potentials gave rise to mirrors, when the mirror applied under infinite magnification condition the most favorable values of the mirror is deduced having the following parameters a = 500 volt, b = 0.01 volt, c = 1.05 mm, fo=-1.618 mm, L = 17.8 mm , Cs= 0.42 mm and Cc= 0.42 mm and the most favorable values of the mirror by using Bimurzaev technique is deduced having the following parameters: a = 150 volt, b = 15 volt, L = 14 mm, c = 2.7 mm, Cs= -8.79 mm, Cc= -0.756 mm and fR= 0.831 mm, where the values of the optical properties in the present work have an excellent performance in comparison with those published in the literature.