A lens changes the direction of light by refraction at its surfaces. In the thin-lens approximation, the separation between those surfaces is treated as negligible compared with the other distances in the problem.

Converging and diverging lenses

A converging lens bends paraxial rays that arrive parallel to the principal axis toward a focal point on the far side.

A diverging lens makes those rays spread as though they came from a focal point on the incoming side.

The focal length $f$ is positive for a converging lens and negative for a diverging lens under a common sign convention.

Thin-lens equation

Object distance $d_o$, image distance $d_i$ and focal length satisfy

$$\frac1f=\frac1{d_o}+\frac1{d_i}.$$

Magnification

The transverse magnification is

$$m=\frac{h_i}{h_o}=-\frac{d_i}{d_o}.$$

Approximation

The simple equations assume paraxial rays, a thin lens and a suitable homogeneous surrounding medium. Real lenses can show aberrations because different rays and wavelengths do not follow the ideal model exactly.

Thin lenses provide the basic model for cameras, eyes, microscopes and telescopes.