# Lens Maker Equation Calculator

1/f = (n−1)(1/R₁ − 1/R₂) with diopters, focal length, and converging/diverging classification; R = 0 marks a plano surface.

> Canonical page: https://elysiatools.com/en/tools/lens-maker-equation

- **Category:** Science & Education

- **Keywords:** lens maker equation, focal length, radius of curvature, optical power, diopters, optics

## Overview

The Lens Maker Equation Calculator determines the focal length, optical power in diopters, and converging or diverging behavior of a thin optical lens in air using the standard lens maker's formula 1/f = (n−1)(1/R₁ − 1/R₂).

## Inputs

- **Refractive index n** (number): e.g. 1.5
- **First radius R₁** (number): e.g. 100 (0 = flat)
- **Second radius R₂** (number): e.g. -100 (0 = flat)
- **Length unit** (select)

## When to use

- Designing or verifying thin optical elements like biconvex, biconcave, plano-convex, or meniscus lenses.
- Converting optical surface radii of curvature and glass refractive indices into diopters and focal length.
- Solving physics and optics problem sets involving thin lens curvature sign conventions.

## How it works

- Enter the refractive index (n) of the lens material relative to air.
- Specify the first radius of curvature (R₁) and second radius of curvature (R₂), entering 0 to represent a flat (plano) surface.
- Select your preferred length unit (millimeters, centimeters, or meters).
- The tool computes the curvature difference, optical power in diopters, focal length in the selected unit and meters, and lens classification.

## Use cases

- Optics students verifying textbook calculations for symmetric and asymmetric thin lenses.
- Optical lab technicians checking diopter power and focal length requirements for stock lenses.
- Physics educators demonstrating how changing surface curvature affects real and virtual focal points.

## Frequently asked questions

### How do I specify a flat or plano lens surface?

Enter 0 for either R₁ or R₂; the calculator interprets zero as an infinite radius of curvature.

### What sign convention does this calculator use for surface radii?

A radius is positive if its center of curvature lies on the transmission (outgoing) side and negative if it lies on the incident (incoming) side.

### What optical medium is assumed around the lens?

The calculation assumes the thin lens is surrounded by air with an ambient refractive index of 1.0.

### How is optical power in diopters calculated?

Optical power is calculated as the inverse of the focal length expressed in meters (P = 1/f_meters).

### How does the tool distinguish between converging and diverging lenses?

Lenses with a positive focal length (and positive diopters) are classified as converging, while negative values indicate diverging lenses.

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