Lensformule

Lensformule refers to the mathematical relationship that describes the behavior of light as it passes through a thin lens. The most common representation is the thin‑lens equation:

1/f = 1/v + 1/u

where f is the focal length of the lens, u is the object distance from the lens, and v is the image distance from the lens. This formula is derived under the Gaussian sign convention, which assigns positive values to distances measured along the direction of the incident light and negative values for distances in the opposite direction. In this convention the focal length of a converging lens is positive, whereas that of a diverging lens is negative.

The lensformule is used to predict the position and size of an image produced by a lens. It is complemented by the magnification equation

m = -v/u

which gives the linear magnification (image height divided by object height). A negative sign indicates that a real image formed by a converging lens is inverted relative to the object.

Applications of the lensformule are wide‑ranging: from the design of simple optical instruments such as magnifying glasses and projectors to the precise alignment of cameras, telescopes, microscopes, and corrective eyewear. In optical engineering it is a foundational tool for determining specifications of lens systems, computing focal lengths of compound lenses, and optimizing image quality.

Historically, the lens formula was first formulated by Helmholtz and later refined by Gaussian optics. It remains a standard element of introductory physics and optical science curricula worldwide.