Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens

An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed, using the multi-step differential transform method based on the classical differential transformation method. Numerical results are compared to those obtained by the fourth-order Runge–Kutta method to illustrate the precision and effectiveness of the proposed method. Results are given in explicit and graphical forms.