PhysicsCalcs
Optics

Lens Maker Equation Calculator

Calculate focal length, refractive index, surface radii, optical power, and classify lens shapes using the Lens Maker's equation.

Interactive calculator

Lens Maker Equation Calculator

Calculate focal length, refractive index, surface radii, optical power, and classify lens shapes using the Lens Maker's equation.

Try an example

+convex, −concave (front)

+concave, −convex (back)

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: find focal length, refractive index, missing radius, optical power, or lens type analysis.
  • Use standard sign convention: + for convex front, − for concave front.
  • Click Calculate for results with lens classification.

Table of Contents

Key Takeaways

  • The Lens Maker's equation relates focal length to refractive index and surface radii.
  • Sign convention: R > 0 if center of curvature is to the right of the surface.
  • Biconvex: R₁ > 0, R₂ < 0 (converging). Biconcave: R₁ < 0, R₂ > 0 (diverging).
  • Higher refractive index → shorter focal length → stronger lens.
  • Optical power P = 1/f in diopters measures how strongly the lens bends light.

The Lens Maker's Equation

The Lens Maker's equation is the fundamental relationship in geometric optics that connects a thin lens's focal length to its material properties and geometry. It allows optical designers to choose the right glass and curvatures for any desired focal length.

Formula & Sign Convention

1f=(n−1)(1R1−1R2)\frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)

Where f is the focal length, n is the refractive index, R₁ is the front surface radius, and R₂ is the back surface radius. The Cartesian sign convention: R is positive when the center of curvature is to the right of the surface.

Lens Shapes

ShapeR₁R₂Type
Biconvex+−Converging
Plano-convex+∞Converging
Biconcave−+Diverging
Plano-concave∞+Diverging
Meniscussame signsame signEither

How to Use

  1. Select a mode (focal length, refractive index, missing radius, power, or type).
  2. Enter values with correct signs for the curvature radii.
  3. Click Calculate for results with lens shape classification.

Examples

BK7 symmetric biconvex (R = ±100 mm)

1/f = (1.517 − 1)(1/0.1 − 1/(−0.1)) = 0.517 × 20 = 10.34 m¹; f ≈ 96.7 mm

Diamond plano-convex (R₁ = 50 mm)

1/f = (2.417 − 1)(1/0.05 − 0) = 1.417 × 20 = 28.34 m⁻¹; f ≈ 35.3 mm

FAQ

What is the Lens Maker's equation?›

The Lens Maker's equation — 1/f = (n−1)(1/R₁ − 1/R₂) — relates the focal length f of a thin lens to its refractive index n and the radii of curvature of its two surfaces R₁ and R₂. It assumes the lens is thin and surrounded by air (n₀ = 1).

What are the sign conventions for R₁ and R₂?›

Using the standard convention: R is positive if the center of curvature is to the right of the surface (convex for the front surface), and negative if to the left (concave for the front). For R₂, the convention is reversed: negative for a convex back surface.

How do I model a flat surface?›

A flat (plano) surface has R = ∞. In practice, enter a very large value like 1000 m. The 1/R term becomes negligible, giving zero curvature contribution from that surface.

Does this work for thick lenses?›

The basic Lens Maker's equation is for thin lenses. For thick lenses, the Lensmaker's equation adds a thickness term: 1/f = (n−1)[1/R₁ − 1/R₂ + (n−1)t/(nR₁R₂)], where t is the center thickness.

What glass types are common for lenses?›

Crown glass (BK7, n ≈ 1.517) is the most common optical glass. Flint glass (n ≈ 1.62) has higher dispersion. Fused silica (n ≈ 1.458) is used for UV optics. Specialty glasses like SF11 (n ≈ 1.785) offer even higher index.

Sources

  1. HyperPhysics – Lensmaker's Equation
  2. Wikipedia – Lensmaker's Equation
  3. Edmund Optics – Understanding Optical Specifications
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

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