## Lens approximations and equations

The main features of most optical systems can be calculated with a
few parameters, provided that some approximation is accepted. The
paraxial approximation requires that only rays entering the optical
system at small angles with respect to the optical axis are taken into
account. The thin lens approximation requires the lens thickness to be
considerably smaller than the radii of curvature of the lens surfaces:
it is thus possible to ignore optical effects due to the real thickness
of the lenses and to simplify ray-tracing calculations. Furthermore,
assuming that both object and image space are in the same medium (e.g.
air), we get the following fundamental equation:

where s (s’ ) is the object (image) position with respect to the
lens, customarily designated by a negative (positive) value, and f is
the focal length of the optical system (cf. Fig. 1). The distance from
the object to the front lens is called working distance, while the
distance from the rear lens to the sensor is called back focal distance.
Henceforth, we will be presenting some useful concepts and formulas
based on this simplified model, unless otherwise stated.