Lens Maker Equation Calculator
Calculate the focal length of a lens from its geometry and refractive index
Common values: Glass ≈ 1.5, Water ≈ 1.33, Diamond ≈ 2.42
Positive for convex (toward light), negative for concave
Positive for convex (away from light), negative for concave
Set to 0 for thin lens approximation
How to Use This Calculator
Enter Refractive Index
Input the refractive index of the lens material. Common values: glass ≈ 1.5, water ≈ 1.33, diamond ≈ 2.42.
Enter Radii of Curvature
Input the radii of curvature for both surfaces in meters. Use positive values for convex surfaces (curved toward the light source) and negative for concave surfaces. For plano surfaces, use a very large number or infinity.
Enter Lens Thickness
Input the lens thickness in meters. For thin lenses (thickness much less than radii), you can set this to 0 to use the thin lens approximation.
Calculate
Click the "Calculate Focal Length" button to get the focal length in meters, centimeters, and diopters.
Formula
Thin Lens Approximation
1/f = (n-1)(1/R₁ - 1/R₂)
Thick Lens (General Case)
1/f = (n-1)[1/R₁ - 1/R₂ + (n-1)t/(nR₁R₂)]
Where:
- f = Focal length (in meters)
- n = Refractive index of the lens material
- R₁ = Radius of curvature of first surface (in meters)
- R₂ = Radius of curvature of second surface (in meters)
- t = Lens thickness (in meters)
Sign Convention:
- R₁: Positive if convex toward incident light, negative if concave
- R₂: Positive if convex away from incident light, negative if concave
- f: Positive for converging lenses, negative for diverging lenses
Example Calculation:
For a glass lens (n = 1.5) with R₁ = 0.1 m and R₂ = -0.1 m:
1/f = (1.5 - 1)(1/0.1 - 1/(-0.1))
1/f = 0.5 × (10 + 10) = 10
f = 0.1 m (10 cm)
About Lens Maker Equation Calculator
The lens maker's equation is a fundamental formula in optics that relates the focal length of a lens to its geometry (radii of curvature) and material properties (refractive index). It's essential for designing lenses, understanding optical systems, and calculating how lenses will focus light. This calculator works for both thin lenses (where thickness is negligible) and thick lenses (where thickness must be accounted for).
When to Use This Calculator
- Lens Design: Design lenses with specific focal lengths
- Optical System Design: Calculate focal lengths for optical systems
- Education: Understand how lens geometry affects focal length
- Research: Analyze lens properties and design experiments
- Quality Control: Verify lens specifications
Why Use Our Calculator?
- ✅ Thin and Thick Lenses: Handles both thin lens approximation and thick lens calculations
- ✅ Instant Results: Get accurate focal lengths immediately
- ✅ Multiple Units: Results in meters, centimeters, and diopters
- ✅ Educational: Includes formula explanations and sign conventions
- ✅ 100% Free: No registration required
Common Applications
Camera Lenses: Lens designers use the lens maker's equation to create lenses with specific focal lengths for photography. Different combinations of curvatures and materials allow for various lens designs.
Telescopes and Microscopes: Optical instruments require precise focal lengths. The lens maker's equation helps designers achieve the desired magnification and image quality.
Eyeglasses: Prescription lenses are designed using the lens maker's equation to provide the correct optical power (diopters) for vision correction.
Tips for Best Results
- Use consistent units (meters for all lengths)
- Remember the sign convention: positive R for convex, negative for concave
- For thin lenses, set thickness to 0 for faster calculation
- Positive focal length means converging lens, negative means diverging
- Equal but opposite radii (R₁ = -R₂) create a symmetric lens
- For plano-convex lenses, one radius is infinite (use a very large number)
Frequently Asked Questions
What is the sign convention for radii?
R₁ is positive if the center of curvature is on the side of the incident light (convex toward light). R₂ is positive if the center is on the side away from incident light (convex away from light). This convention ensures that a biconvex lens (both surfaces convex toward center) has R₁ positive and R₂ negative.
When can I use the thin lens approximation?
The thin lens approximation is valid when the lens thickness is much smaller than the radii of curvature. For most practical purposes, if thickness is less than about 10% of the smallest radius, the thin lens equation is accurate enough.
How do I handle a plano surface?
For a plano (flat) surface, the radius of curvature is infinite. In the calculator, use a very large number (like 1,000,000) to approximate infinity. The 1/R term will then be approximately zero.
What creates a converging vs diverging lens?
A converging lens (positive focal length) typically has both surfaces convex toward the center, or one surface significantly more curved than the other. A diverging lens (negative focal length) typically has both surfaces concave toward the center, or is thinner at the center than at the edges.
Does the equation work for all lens shapes?
The lens maker's equation works for spherical surfaces. For aspherical surfaces, more complex calculations are needed. However, most lenses use spherical surfaces, so this equation is widely applicable.