Relation for combination of two thick lenses

[justawebuser]

Simple lenses are subject to the optical aberrations discussed above. In many cases these aberrations can be compensated for to a great extent by using a combination of simple lenses with complementary aberrations. A compound lens is a collection of simple lenses of different shapes and made of materials of different refractive indices, arranged one after the other with a common axis.

The simplest case is where lenses are placed in contact: if the lenses of focal lengths f1 and f2 are "thin", the combined focal length f of the lenses is given by

Since 1/f is the power of a lens, it can be seen that the powers of thin lenses in contact are additive.

If two thin lenses are separated in air by some distance d, the focal length for the combined system is given by

So what if we have two thick lenses?
Thanks in advance ,

 

[UltrafastPED]

More complicated ... here is one way: http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/sysmat.html