Lensmaker's Equation Calculator
Calculate focal length from lens geometry using 1/f = (n−1)(1/R₁ − 1/R₂).
For a flat surface: R = ∞ (enter 1e12). Sign: center of curvature to the right = positive.
What Is Lensmaker's Equation Calculator?
The formula Calculate focal length from lens geometry using 1/f = (n−1)(1/R₁ − 1/R₂)., is fundamental to this topic in physics.
This relationship is derived from first principles and applies broadly across scales and materials.
Engineers and scientists use this daily. The calculator automates arithmetic so you can focus on physical reasoning.
Ensure SI units throughout for correct results.
Formula Reference Table
| Solve For | Formula | Notes |
|---|---|---|
| Lensmaker's equation | 1/f = (n−1)(1/R₁ − 1/R₂) | f in m |
| Biconvex (R₁>0, R₂<0) | 1/f = (n−1)(1/R + 1/R) = 2(n−1)/R | Converging |
| Plano-convex (R₂=∞) | 1/f = (n−1)/R₁ | One flat side |
| Biconcave | R₁<0, R₂>0 | Diverging; f < 0 |
| Lens power | P = 1/f | Diopters (P = 1/f in meters) |
| Thin lenses combined | P_total = P₁ + P₂ | In contact; P in diopters |
3 Worked Examples
n=1.5, R₁=+10 cm, R₂=−10 cm.
- 1/f = (1.5−1)(1/0.1 − 1/(−0.1)) = 0.5×(10+10) = 10 m⁻¹
- f = 1/10 = 0.10 m = 10 cm
n=1.52, R₁=+5 cm, R₂=∞.
- 1/f = (1.52−1)(1/0.05 − 0) = 0.52×20 = 10.4 m⁻¹
- f = 1/10.4 = 9.6 cm
Biconvex R=5 cm each, measured f=4.5 cm.
- 1/f = (n−1)(1/R₁−1/R₂) = (n−1)×(20+20) = (n−1)×40
- (n−1) = 1/(0.045×40) = 0.556 → n = 1.556
Real-World Applications
Common Mistakes to Avoid
SI units required.
Use correct form for geometry.
Ideal conditions assumed.
Check conventions.
Verify squared/sqrt.
Frequently Asked Questions
Related Physics Calculators
Formula Explorer connections
Interpretation: This relationship connects light propagation, geometry, wavelength, refraction, interference or image formation. Assumption: Use a consistent sign convention and units. Paraxial rays, thin elements, coherent light, vacuum wavelength or ideal optical components may be assumed.