> For the complete documentation index, see [llms.txt](https://simplemetalens.gitbook.io/docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://simplemetalens.gitbook.io/docs/smd-pro/topical-discussions/lens-equation.md).

# Lens Equation (Gaussian formula)

The figure below describes image formation by a thick, positive lens for paraxial rays. The relationship between the object and image is given by the Gaussian formula (aka. lens maker's equation). SMD PRO uses the sign convention where s < 0 for real objects, s > 0 for virtual objects, s’ < 0 for virtual images, and s’ > 0 for real images.

$$
Magnification \   (m) ={ h'\over h} = {ns'\over n's}
$$

<figure><img src="https://1531699250-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FFaobmSDh9ItlF3pOiSuB%2Fuploads%2Fgit-blob-391f09995d7bdf5b235b1c8d0ea921dac232ce91%2Fknowledgebase_lensequation.png?alt=media" alt="Minsu Oh, Simple Metalens"><figcaption><p>Imaging with a lens. n, n<sub>lens</sub>, and n': refractive indices (real part) of object space, lens, and image space, respectively. P and P': principal planes on the object and image sides, respectively. s and s’: object and image positions with respect to their corresponding principal planes, respectively. EFL and EFL’: effective focal lengths on the object and image sides, respectively.</p></figcaption></figure>