Lensmaker's Equation Calculator

How to Use This Calculator

1. Enter refractive index n of the lens material (e.g. 1.5 for crown glass).
2. Enter R₁ (front surface radius) and R₂ (back surface radius). Use sign convention: + if center of curvature is right, − if left. Enter 0 for a flat surface.
3. Enter thickness d (use 0 for thin lens approximation).
4. Results show focal length and lens power.
5. Use Presets tab for common lens shapes.

Formula

Example

Frequently Asked Questions

• What is the lensmaker's equation? ▼
  1/f = (n−1)[1/R₁ − 1/R₂ + (n−1)d/(nR₁R₂)], where n = refractive index, R₁ = front radius, R₂ = back radius, d = center thickness. For a thin lens (d ≈ 0), the last term vanishes: 1/f = (n−1)(1/R₁ − 1/R₂).
• What sign convention is used for radii? ▼
  R is positive if the center of curvature is to the right of the surface (as light travels left to right). For a standard biconvex lens: R₁ > 0 (front surface curves toward light) and R₂ < 0 (back surface curves away). A flat surface has R → ∞ (enter 0 in the calculator).
• What is a plano-convex lens? ▼
  One flat surface (R = ∞) and one convex surface. For 1/f = (n−1)/R₁ (since 1/R₂ = 0). These are common in optical systems because they reduce spherical aberration when oriented correctly (curved side facing the collimated beam).
• What is the Abbe number? ▼
  The Abbe number V_d = (n_d − 1)/(n_F − n_C) measures dispersion — how much refractive index varies with wavelength. Crown glass: V_d ≈ 64 (low dispersion). Flint glass: V_d ≈ 36 (high dispersion). Achromatic doublets pair a crown and flint lens to cancel chromatic aberration.
• What is dispersive power? ▼
  Dispersive power ω = 1/V_d. Higher ω means more chromatic aberration (different colors focus at different distances). Achromat design requires ω₁/f₁ + ω₂/f₂ = 0.

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