Lens

A lens element is a component made of an optical transparent material (usually glass) with two optical active surfaces.
“optical transparent” does not necessarily mean that the component is transparent for human eyes!
For example are lenses made of Germanium not transparent for humans. For certain cameras they are transparent however.
Lenses can be used to focus light
Lens_and_wavefronts[1]
The main effect of lenses is that they map object points to image points.
Let say we have two object points, for example the Top T0 and the bottom B0 of a vase. A two element compound lens works like this :
The object points T0 an B0 are mapped to image points T1 and B1 by lens element number 1. The lens elements are numbered starting from object side.
The images T1 and B1 then become the new “object points” of lens element 2 and map T1 and B1 to “images of image” of T0 and T0, called T2 and B2″.

A lens with 10 lens elements accordingly generates sequences
T0->T1->T2->… -> T10
and
B0->B1->B2->….-> B10

The image produced by a lens can be in front or behind the lens.
It can be smaller or bigger than the object.
Of course we want images of trees to be smaller than trees.
Image of microscopic details we of course want to be larger than the details.