Lensmaker's Equation⚠ unverified
Physics / Optics · Thin-lens focal length from the lensmaker's equation
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| n | n | — | 1.5 | Refractive index |
| R1 | R1 | m | 0.1 | First surface radius |
| R2 | R2 | m | -0.1 | Second surface radius |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| f | f | m | Focal length |
The science & history
Understanding the Parameters
- $n$ — higher index → stronger lens for the same radii.
- $R_1$, $R_2$ — sign convention matters; biconvex often $R_1>0$, $R_2<0$ so both terms add.
- $f$ — positive for converging thin lens in the usual convention.
Derivation (Approaching a Proof)
Paraxial refraction at a single spherical surface: $n_1/s + n_2/s' = (n_2-n_1)/R$. Cascading two surfaces with thin-lens separation → 0 and $n_1=n_2=1$ outside yields the maker’s formula.
History
Lensmakers’ formula is classical geometric optics (Gauss, 19th-century lens design).
Related Concepts: Lens Power, Lens Magnification, Mirror Focal Length
Notes: Registry calculator lensmaker-formula (unverified). Thin lens in air; confirm sign
convention in ToolBox.