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 *subject 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, its thickness along the optical axis (drawn as a horizontal blue line) is small compared to its focal length.

The lens equation describes the relation between focal length **f** of the lens, *subject distance* **g** between subject and lens and *image distance* **h** between lens and image sensor when the image of the subject 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*. See how **g** and **h** are adjusted when the lens is focused in the next section.