# Lensmaker's equation

## Description

A lens is a transmissive optical device which affects the focusing of a light beam through refraction. A simple lens consists of a single piece of material, while a compound lens consists of several simple lenses (elements), usually along a common axis.

If the lens is biconvex or plano-convex, a collimated beam of light passing through the lens will be converged (or focused) to a spot behind the lens. In this case, the lens is called a positive or converging lens. If the lens is biconcave or plano-concave, a collimated beam of light passing through the lens is diverged (spread); the lens is thus called a negative or diverging lens.

Lensmaker Equation is used to determine whether a lens will behave as a converging or diverging lens based on the curvature of its faces and the relative indices of the lens material and the surrounding medium. It is used for determining the focal length of a thin lens (thickness = 0) with radii of curvature r1 and r2.

The focal length f is positive for converging lenses, and negative for diverging lenses.

## Variables

f | Focal length (m) |

n | Refractive index of the lens material (dimensionless) |

R1 | Radius of curvature of the lens surface closest to the light source (m) |

R2 | Radius of curvature of the lens surface farthest from the light source (m) |

d | Thickness of the lens (m) |