Configure the lens
Session history
How radius of curvature determines lens power
Understanding optical power
Optical power measures how strongly a lens changes the direction of paraxial light. Power is expressed in diopters. One diopter equals one inverse meter.
A positive power normally describes a converging lens. A negative power describes a diverging lens. The reciprocal of power gives focal length in meters for a thin lens in air.
Why curvature matters
A small radius creates a steep surface. Steeper surfaces usually produce stronger refraction. A large radius produces a flatter surface and generally weaker power.
A plane surface has infinite radius. Its curvature is zero. Therefore, its direct curvature contribution is also zero.
Thin-lens maker equation
The formula uses the lens index, surrounding-medium index, and both signed radii. All radii must be expressed in meters. The output is then obtained in inverse meters or diopters.
The thin model assumes negligible distance between the refracting surfaces. It is useful for quick estimates and many educational problems.
Thick-lens maker equation
A thick lens separates its refracting surfaces by a measurable center thickness. This separation changes equivalent power and focal reference positions.
Thick-lens analysis also introduces principal planes. Effective focal length is measured from those planes. Front and back focal distances are measured from the physical lens vertices.
Single spherical surface power
A single refracting interface has power when its adjacent media have different indices. A plane interface can bend oblique rays, but its paraxial surface power is zero.
Sign convention used
Light is assumed to travel from left to right. A radius is positive when its center lies rightward from the surface. A radius is negative when its center lies leftward.
A conventional biconvex lens commonly uses positive R1 and negative R2. A conventional biconcave lens commonly uses negative R1 and positive R2.
How to use this calculator
Step one: choose the mode
Select thin lens for quick estimates. Select thick lens when center thickness matters. Reverse modes solve missing design variables from a target power.
Step two: select a shape
Choose a preset or keep the custom option. Presets load typical signs and sample radii. Verify the orientation before calculating.
Step three: enter geometry
Enter R1, R2, center thickness, and clear aperture. Select the correct units. Mark a surface as plane instead of entering zero.
Step four: set optical properties
Select a material or enter a custom refractive index. Choose the surrounding medium. Enable approximate dispersion only when wavelength comparison is useful.
Step five: review warnings
Check curvature signs, aperture limits, edge estimates, and unusually high powers. Validate professional work using complete optical design software.
Thin versus thick lens results
Thin and thick results can be nearly identical for small center thickness. Differences grow with stronger curvature, larger thickness, and higher refractive index.
The thick model is not automatically a complete real-lens model. It still assumes paraxial rays and spherical centered surfaces.
Surface power interpretation
The first surface power depends on the transition from medium to lens. The second surface power depends on the transition from lens back to medium.
Surface powers cannot always be added directly for thick lenses. Translation through the lens material couples the two surfaces.
Focal lengths and vertex powers
Effective focal length describes the system from its principal planes. Front and back focal distances start at the physical vertices.
Ophthalmic work often uses back vertex power because spectacle lenses are positioned relative to the eye. This calculator reports both front and back vertex estimates.
Sagitta and edge thickness
Sagitta measures surface depth over a chosen semi-diameter. It is calculated from spherical geometry and signed for display.
The edge-thickness result is an approximate geometry check. Real production design must include bevels, minimum thickness, mounting, safety, and process allowances.
Wavelength and dispersion
Refractive index changes with wavelength. This produces chromatic focal shift. The calculator provides an educational estimate based on Abbe number.
That estimate is not a substitute for a Sellmeier equation or manufacturer glass catalog. Use catalog coefficients for precision optical design.
Tolerance analysis
Manufacturing variations change power. Radius, index, and thickness errors can each contribute. The sensitivity table recalculates power at simple plus-and-minus limits.
It is not a statistical Monte Carlo analysis. It also does not include correlated errors. Use dedicated tolerance software for production acceptance limits.
Important limitations
The calculator assumes centered spherical surfaces and paraxial rays. It does not optimize spherical aberration, coma, astigmatism, distortion, or field curvature.
It does not trace finite ray bundles through stops or multi-element assemblies. It also does not model coatings, birefringence, polarization, diffraction, or thermal gradients.
Lens power calculator FAQ
Why must radii be converted to meters?
Diopters are inverse meters. Meter-based radii keep the lensmaker equation dimensionally consistent.
Can I enter zero for a plane surface?
Use the plane-surface checkbox. Zero radius represents infinite curvature, not a flat surface.
Why is a biconvex second radius negative?
Under the selected Cartesian convention, the second center of curvature lies leftward from the second vertex.
What does negative focal length mean?
It usually indicates a diverging optical system with a virtual paraxial focus.
Does reversing a lens change its equivalent power?
Equivalent power is generally unchanged in the same surrounding medium, but front and back focal distances can change.
Why do thin and thick powers differ?
The thick model includes translation between separated refracting surfaces.
Can this calculate an aspheric lens?
No. The power calculation uses spherical paraxial curvature only.
Can I calculate a lens immersed in water?
Yes. Select water or enter a custom medium index.
What is the Abbe number used for?
It indicates dispersion and supports the calculator's approximate wavelength-index estimate.
Is the edge thickness exact?
No. It is a spherical geometry estimate and excludes bevels, tolerances, mounting, and safety rules.
Can the calculator solve a missing radius?
Yes. Choose solve R1 or solve R2 and enter the target power plus remaining parameters.
What happens when lens and medium indices match?
Refraction disappears in the ideal model, so lens power approaches zero.
What is a principal plane?
It is a paraxial reference plane from which effective focal distances are measured.
Can this replace commercial optical design software?
No. Use it for education, estimates, checking, and early design exploration.
Optical glossary
A compact measure of visible-light dispersion.
Distance from the rear vertex to the rear focal point.
Power referenced to the rear vertex.
Axial separation between front and back vertices.
Usable optical diameter through which rays pass.
The reciprocal of signed radius.
One inverse meter of optical power.
Focal length measured from the principal plane.
Distance from the front vertex to the front focal point.
Relationship between index, curvature, thickness, and power.
A ray near the axis with a small angle.
Reference plane used in first-order optical imaging.
Signed distance from a surface vertex to its curvature center.
Direction change caused by refractive-index transition.
Surface depth from chord plane to spherical surface.
Paraxial power of one refracting interface.