Lensmaker's Equation Calculator
Focal length and power of a lens from its glass, the two radii of curvature and the thickness, in air or in another medium.
Results
What this tool does
The lensmaker's equation tells you how a piece of glass becomes a lens: what matters is its refractive index and how curved each face is. The sign convention trips most people up: a radius is positive when its centre lies beyond the surface, so a common biconvex lens has R₁ positive and R₂ negative; enter 0 for a flat face. A plano-convex lens of ordinary crown glass (n ≈ 1.517) has a focal length of about twice its radius. The same lens under water loses most of its power, because what counts is the index relative to the surroundings, which is why your eyes see blurred when you open them while swimming.
Formula
1/f = (n − 1) [1/R₁ − 1/R₂ + (n − 1) d ÷ (n R₁ R₂)]
Variables
| Symbol | Meaning | Unit |
|---|---|---|
n | Refractive index of the glass | — |
r1 | Radius of the first surface (0 = flat) | mm |
r2 | Radius of the second surface (0 = flat) | mm |
d | Centre thickness (0 = thin lens) | mm |
nm | Index of the surrounding medium (air = 1) | — |
F | Focal length | mm |
D | Optical power | D |
TY | Kind of lens | — |
Worked example
- Refractive index of the glass1.5168
- Radius of the first surface (0 = flat)100 mm
- Radius of the second surface (0 = flat)-100 mm
- Centre thickness (0 = thin lens)0 mm
- Index of the surrounding medium (air = 1)1
- Focal length96.75 mm
- Optical power10.336 D
- Kind of lensConverging lens (positive)
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.