A *converging lens* is characterized by collecting parallel light rays in a focal point **F**. As a consequence, light emitted from a point in an *object plane* (parallel to the lens, at a finite distance) is collected in a single point in a corresponding *image plane* (also parallel to the lens). For a *thin converging lens* where the thickness along the optical axis (drawn as a horizontal blue line) is small compared to its focal length, the situation looks as shown in fig. 1.

The lens equation describes the relation between focal length **f** of the lens, object distance **g** (between object and lens) and image distance **h** (between lens and image sensor or film) when the image of the object appears sharp. It can be derived as follows.

By similar triangles along the purple ray passing through **F** left of the lens, we have

G / (g - f) | = | H / f | (L1) |

Likewise, by similar triangles along the purple ray through **F** right of the lens, we get

G / f | = | H / (h - f) | (L2) |

Solving both equations for G / H results in

(g - f) / f | = | f / (h - f) | (L3) |

After some simple algebraic transformations, the equation looks like this

g h | = | f h + f g | (L4) |

Finally, after division by f g h, we get the well-known form

1 / f | = | 1 / g + 1 / h | (L5) |

This equation is known as the *lens equation* or *thin lens formula*. It is a surprisingly powerful tool to calculate e.g. magnification or depth of field of a lens.