The lens maker formula is a mathematical formula that describes the relationship between the focal length, refractive index, and curvature of a lens. It is used to design lenses for various applications, including eyeglasses, telescopes, cameras, and microscopes.


The lens maker formula is derived from the thin lens equation and the lens law. The thin lens equation is given by:

1/f = (n - 1) (1/R1 - 1/R2)

where f is the focal length, n is the refractive index of the lens material, R1 is the radius of curvature of the first lens surface, and R2 is the radius of curvature of the second lens surface. The lens law states that:

n1 sinθ1 = n2 sinθ2

where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.


The lens maker formula is given by:

1/f = (n - 1) [(1/R1) - (1/R2) + ((n - 1) d)/(n R1 R2)]

where d is the thickness of the lens.


The lens maker formula takes into account the thickness of the lens, which is not considered in the thin lens equation. The formula shows that the focal length of a lens depends on the refractive index of the lens material, the radius of curvature of the lens surfaces, and the thickness of the lens.

The formula also shows that the curvature of the lens surfaces affects the focal length of the lens. A lens with a flatter curvature will have a longer focal length, while a lens with a steeper curvature will have a shorter focal length.


The lens maker formula is an important tool for designing lenses for various applications. By adjusting the refractive index, curvature, and thickness of a lens, it is possible to achieve a desired focal length and optical performance.