This puts a fundamental limitation on the geometry of an optics system. If an optical system of a given size is to produce a particular magnification, then there is only one lens position that will satisfy that requirement. On the other hand, a big advantage is that one does not need to make a direct measurement of the object and image sizes to know the magnification; it is determined by the geometry of the imaging system itself.

Let’s now go back to our ray tracing diagram and look at one more set of line segments. In Figure 3, we look at the optical axis and the ray through the front focus. Again looking at similar triangles sharing a common vertex and, now, angle η, we have

**y**_{2}/f = y_{1}/(s_{1}-f).

Rearranging and using our definition of magnification, we find

**y**_{2}/y_{1} = s_{2}/s_{1} = f/(s_{1}-f).

Rearranging one more time, we finally arrive at

**1/f = 1/s**_{1} + 1/s_{2}.

This is the Gaussian lens equation. This equation provides the fundamental relation between the focal length of the lens and the size of the optical system. A specification of the required magnification and the Gaussian lens equation form a system of two equations with three unknowns: f, s_{1}, and s_{2}. The addition of one final condition will fix these three variables in an application.

This additional condition is often the focal length of the lens, f, or the size of the object to image distance, in which case the sum of s_{1} + s_{2} is given by the size constraint of the system. In either case, all three variables are then fully determined.