Lens Maker Equation Calculator

The lens maker's equation relates the focal length of a thin lens to its refractive index and the radii of curvature of its two surfaces: 1/f = (n-1)(1/R1 - 1/R2). Here n is the refractive index of the lens material relative to the surrounding medium (usually air), R1 is the radius of curvature of the first surface (the one the light hits first), and R2 is the radius of the second surface.

Using the standard (Cartesian) sign convention: R is positive if the center of curvature is to the right of the surface (center of curvature on the transmission side), and negative if it is to the left. For a biconvex lens: R1 > 0 and R2 < 0. For a plano-convex lens with flat first surface: R1 = infinity and R2 < 0, giving 1/f = (n-1)/|R2|.

The lens maker's equation applies to any thin lens in a uniform medium: biconvex (R1 > 0, R2 < 0), biconcave (R1 < 0, R2 > 0), plano-convex (R1 = flat = infinity, R2 < 0), plano-concave, meniscus (both same sign), and more. The sign of f determines whether the lens is converging (f > 0) or diverging (f < 0).

A flat (plane) surface has infinite radius of curvature. In the formula, 1/R1 or 1/R2 becomes zero for a flat surface. For a plano-convex lens with the flat surface first, R1 = infinity (enter a very large number, or the calculator handles it as 0) and R2 is the radius of the curved surface.

Higher refractive index glass produces a shorter focal length (more powerful lens) for the same curvatures. Doubling n-1 halves the focal length. This is why high-index (n~1.74) lenses for eyeglasses can be made thinner and lighter than standard (n~1.52) lenses with the same optical power.