A new theoretical schematic model of the human eye is introduced. The new model considers that the human eye crystalline is a gradient index lens composed by two oblate half spheroids of different heights. By modifying the spherically symmetric Luneburg model for a gradient index lens, we created a model for the anterior and posterior half spheroids matching the corresponding geometric and gradient index boundary conditions at the plane of fusion of the spheroids. We tested the imaging capabilities of our model and found that it is more realistic compared with those reported in the literature concluding that the gradient index is dynamic and cannot be modeled by one single explicit equation.