Lens Maker Equation Calculator
Design and analyze simple lenses. Input the curvature of each surface, the material's refractive index, and thickness to find the focal length.
1/f = (n-1) × (1/R₁ - 1/R₂ + (n-1)d/(n×R₁×R₂))
Glass: 1.5, Water: 1.33, Diamond: 2.42
Use 0 for thin lens approximation
Positive if center is on outgoing side
Negative if center is on incoming side
Sign Convention:
- R is positive if the center of curvature is on the outgoing side
- R is negative if the center of curvature is on the incoming side
- Positive focal length = converging lens
- Negative focal length = diverging lens
How the Lens Maker Equation Calculator Works
Enter the radii of curvature for both lens surfaces (R₁ and R₂), the lens material's refractive index, and the lens thickness. Use positive values for convex surfaces and negative for concave surfaces (sign convention matters).
The calculator applies the lens maker equation: 1/f = (n-1)[1/R₁ - 1/R₂ + (n-1)d/(nR₁R₂)], where f is focal length, n is refractive index, R₁ and R₂ are surface radii, and d is thickness. For thin lenses, the thickness term is negligible.
Results show the focal length with sign (positive for converging, negative for diverging). Lens power in diopters is also calculated. A ray diagram shows how parallel rays converge or diverge through the lens.
When You'd Actually Use This
Eyeglass prescription design
Design corrective lenses. Optometrists specify power in diopters. Lens makers use this equation to grind lenses with correct curvature.
Camera lens design
Calculate focal lengths for camera lenses. Multi-element lenses combine multiple lens elements to correct aberrations while achieving desired focal length.
Telescope and microscope optics
Design objective and eyepiece lenses. Calculate magnification from focal lengths. Match lens combinations for optimal image quality.
Physics lab experiments
Predict lens behavior in optics experiments. Verify the lens maker equation by measuring focal length and comparing to calculated values.
Laser beam focusing
Select lenses for laser applications. Calculate focal length needed to focus a laser to a specific spot size at a given distance.
Contact lens fitting
Understand contact lens optics. Base curve radius affects how the lens fits the cornea. Power depends on both curvature and material.
What to Know Before Using
Sign convention is critical.Convex surface (bulging toward incoming light): positive R. Concave surface: negative R. Wrong signs give wrong focal length.
Positive f means converging lens.Convex lenses (thicker in middle) have positive focal length. Concave lenses (thinner in middle) have negative focal length.
Diopters are inverse meters.Power P = 1/f (in meters). A 50 mm lens has power 1/0.05 = 20 diopters. Eyeglass prescriptions are in diopters.
Refractive index depends on wavelength.Glass has different n for different colors. This causes chromatic aberration - different colors focus at different points.
Pro tip: For a symmetric biconvex lens (R₁ = -R₂ = R) in air, the equation simplifies to 1/f = 2(n-1)/R. This quick estimate works for many common lenses.
Common Questions
What if both surfaces are flat?
R = infinity for flat surfaces. 1/R = 0. A flat piece of glass has infinite focal length - it doesn't focus light (ignoring thickness effects).
Why does thickness matter?
Thick lenses have additional refraction inside the material. The thickness term accounts for this. For thin lenses (d ≪ R), it's negligible.
Can focal length be negative?
Yes. Negative focal length means diverging lens. Parallel rays appear to diverge from a virtual focus on the incoming side.
What's a meniscus lens?
Both surfaces curve the same direction (both convex or both concave from the same side). Can be converging or diverging depending on curvatures.
Does this work for mirrors?
No, this is for refractive lenses. Mirrors use different equations. For spherical mirrors: 1/f = 2/R (half the radius of curvature).
How accurate is this equation?
It's exact within paraxial approximation (small angles). For large apertures or precise work, ray tracing software accounts for spherical aberration.
What about compound lenses?
Use the lens equation for each element, then combine. For thin lenses in contact: 1/f_total = 1/f₁ + 1/f₂ + ... Powers add directly.
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