# Equation of lens manufacturers

Descartes is credited with discovering the lens makers equation

Historically, this discovery was attributed to René Descartes who, in addition to being a physicist, was a philosopher and mathematician. This equation, called “from the lens makers”, is also known as “Halley’s equation”. It relates the focal length ** f** of a thin lens to the radii of curvature

**and**

*R*_{1}**of its faces, the absolute refractive index (**

*R*_{2}

*n**) of the material the lens is made of and the absolute refractive index (*

_{lens}

*n**) of the medium in which the lens is immersed:*

_{half}*If the curvature face is convex – R > 0, that is, the sign of the radius of curvature R will be positive.
If the curvature face is concave – R < 0, that is, the sign of the radius of curvature R will be negative* .

When the lens is in the air, *n _{lens}* = 1, a biconvex lens will be converging as the distance

*f*is positive. However, if we place this lens in a liquid whose index of refraction is greater than that of the lens (

*n*), its focal length will be negative, indicating that the lens becomes divergent in this medium. Likewise, a diverging lens immersed in this liquid will become converging.

_{medium}> n