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 R 1 and R 2 of its faces, the absolute refractive index ( n lens ) of the material the lens is made of and the absolute refractive index ( n half ) of the medium in which the lens is immersed:
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 medium > 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.