What this calculator does
Lensmaker's equation works out focal length of a lens from its surface curvatures, thickness and refractive index. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formula1/f = (n−1)[1/R1 − 1/R2 + (n−1)d/(nR1R2)]; thin lens: set d = 0
The inputs explained
| Field | What to enter |
|---|---|
| Refractive index of the lens | A number. Starts at 1.5. |
| Radius of curvature R1 (+ if convex toward the light) (m) | A number, measured in m. Starts at 0.1. |
| Radius of curvature R2 (− if convex away from the light) (m) | A number, measured in m. Starts at -0.1. |
| Lens thickness (0 for thin-lens approximation) (m) | A number, measured in m. Starts at 0.01. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with refractive index of the lens
Every other input is held at the calculator’s starting values while refractive index of the lens varies. Select any row to load that scenario into the calculator.
How the answer changes with refractive index of the lens
| Refractive index of the lens | Focal length | Optical power | Thin-lens approximation (d=0) |
|---|---|---|---|
| 0.75 | -0.1967 m | -5.083 D (dioptres) | -0.2000 m |
| 1.13 | 0.3868 m | 2.585 D (dioptres) | 0.3846 m |
| 1.5 | 0.1017 m | 9.833 D (dioptres) | 0.1000 m |
| 2.25 | 0.0411 m | 24.306 D (dioptres) | 0.0400 m |
| 3 | 0.0259 m | 38.667 D (dioptres) | 0.0250 m |
| 4.5 | 0.0149 m | 67.278 D (dioptres) | 0.0143 m |