The thin lens formula

The geometry of the ray diagram for a thin lens or mirror leads at once to a formula that connects the image distance (v) with the object distance (u) and the focal length (f). The derivation relies on the properties of similar triangles and is approximate in a real case (ie. the formula is only as accurate as the ray diagram it is derived from).

The same formula applies to all configurations if a sign convention is followed. The preferred convention is the assignment of a positive value to images, objects, and focal lengths, defined as real (with rays passing through them), and a negative value to virtual images, focal lengths, and objects.

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