In this article we introduce a new approach for obtaining Lorentz transformations. It is based on tracking light that is emitted from an object that reaches two stationary observers who are in motion relative to one other. This new approach, based on known physical principles and not on an axiom, makes the Lorentz transformations more understandable. In addition, it reveals the meaning of the constancy of the speed of light as well as the meaning of the results of the Special Theory of Relativity. The new approach also reveals that Lorentz transformations for an object found at a general point (x',y') at the coordinate system, cannot be achieved as a superposition of the transformations of the coordinates (x',0) and (0,y'). In this case we need to take into account the time delay between cases. Light aberration, the Doppler effect, time dilation and length contraction are considered within the new approach of obtaining Lorentz transformations.