The Gaussian Imaging Equation
1 1 1
 
l l f
(for thin lens in air):
(In accordance with the sign rules.)
f
l
l’
Unfortunately, this equation is often (perhaps usually) written without regard to
the sign rules: e.g., 1  1  1 , where o and i refer to the ‘object’ and ‘image’
o
i
f
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.
Easy way to remember the Imaging Equation:
l
l’
i
o
K=1/f
At the lens, the incoming wave from the object point has curvature
1
l
1
The lens adds curvature K  to the wave;
f
So the outgoing wave has curvature 1  1  1 , which is the correct equation.
l
l
f
(Note that curvatures, like any other quantities, only add correctly if their
signs are considered.