1. The Gaussian Imaging Equation
(In accordance with the sign rules.) l l’ f
Unfortunately, this equation is often (perhaps usually) written without regard to the sign rules: e.g., , where o and i refer to the ‘object’ and ‘image’
distance as always positive numbers.
This leads to confusion and makes the correct equation harder to remember.
Ignoring the sign rules works when considering a single, positive lens, but leads to confusion and errors when trying to trace a chain of intermediate images through an optical system.
Ignoring the sign rules works when considering a single, positive lens, but leads to confusion and errors when trying to trace a chain of intermediate images through an optical system.

2. Easy way to remember the Imaging Equation:
K=1/f l l’
At the lens, the incoming wave from the object point has curvature
The lens adds curvature to the wave;
So the outgoing wave has curvature , which is the correct equation.
(Note that curvatures, like any other quantities, only add correctly if their signs are considered.