Lens Maker Equation Calculator

The Lens Maker Equation relates the focal length of a thin lens to the radii of curvature of its two surfaces and the refractive index of the lens material. For a lens in a medium, it is: 1/f = (n_lens/n_medium − 1) × (1/R1 − 1/R2). It allows optical engineers to design lenses with a specific focal length by choosing the right geometry and material.

By the standard sign convention, a radius R1 is positive when the center of curvature of the first surface lies to the right of the surface (convex toward incoming light), and negative when it lies to the left (concave). R2 follows the same convention for the second surface. A biconvex lens has R1 > 0 and R2 < 0.

A flat surface has an infinite radius of curvature. To simulate it in this calculator, enter a very large number such as 1,000,000 mm (1×10⁶) for R1 or R2. The term 1/R then effectively becomes zero, which is the mathematically correct treatment.

Lens power (D) is the reciprocal of focal length measured in meters: D = 1/f(m). It is measured in diopters (D). A positive power means a converging lens; a negative power means a diverging lens. Eyeglass prescriptions are written directly in diopters.

The simple magnification formula M = D × 0.25 + 1 gives the magnifying power when an object is placed at the standard near-point distance of 25 cm (0.25 m). This is the magnification achievable when using the lens as a simple magnifier with the image at infinity.

A lens is converging (positive lens) when its focal length is positive — it bends parallel rays to a real focus on the far side. A lens is diverging (negative lens) when the focal length is negative — it spreads rays so they appear to originate from a virtual focus. The result depends on the combination of curvature signs and the refractive index.

No. This calculator implements the thin lens approximation, which assumes the lens thickness is negligible compared to the radii of curvature. For thick lenses, an additional term involving lens thickness d must be added: (n − 1) × d / (n × R1 × R2). For most practical optical design involving standard eyewear or camera lenses, the thin lens formula gives a good first approximation.

Common values: crown glass ≈ 1.52, flint glass ≈ 1.62, borosilicate glass ≈ 1.47, polycarbonate ≈ 1.59, acrylic (PMMA) ≈ 1.49, water ≈ 1.33, and diamond ≈ 2.42. Higher refractive index materials allow thinner lenses for the same focal length.