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Optical Lens Focal Length Calculator (Lensmaker and Thin Lens)

Focal length ties lens geometry to what the optic does on the bench. This calculator applies the lensmaker equation to surface radii and glass index, then uses the thin lens equation to give image distance and magnification, with f-number and the diffraction-limited Airy spot for your wavelength.

Your numbers

Lens material

Refractive index at your operating wavelength. Index changes with wavelength, so check the glass catalog.

Radius of surface 1 (R1)

Positive when the center of curvature is on the outgoing side. Biconvex lens: R1 positive.

Radius of surface 2 (R2)

Biconvex lens: R2 negative. Plano surface: use a very large number such as 1000000.

Object distance

Distance from lens to object. Use a large value for a distant source.

Clear aperture diameter

Used for f-number and spot size.

Wavelength

Vacuum wavelength for the diffraction-limited spot estimate.

Your results

Focal length (mm)

49.8259

Thin lens lensmaker equation.

f-number

1.9616

Focal length divided by clear aperture.

Optical power (diopters)

20.0699

Reciprocal of focal length in meters.

Image distance (mm)

66.3574

From the thin lens equation. Negative means a virtual image on the object side.

Magnification

-0.3318

Negative means an inverted real image.

Airy disk diameter (um)

3.0298

Diffraction-limited spot diameter to the first dark ring for a uniformly filled aperture.

Thin lens approximation: ignores center thickness, principal plane offsets, aberrations and wavelength dispersion. Use optical design software or the lens vendor data for tolerance-critical systems.

Save results:

Image distance vs object distance

Sweeps Object distance from 60 to 600, holding your other inputs fixed.

Optical specs in your ERP item master

Optional: an expert look at storing optical attributes and inspection results against item and lot records.

Optional. The tool and every export work without this. No spam.

How to use it

Pick the lens material, then enter R1 and R2 using the standard sign convention: a surface is positive when its center of curvature lies on the outgoing side of the light. A biconvex lens therefore has R1 positive and R2 negative. For a plano-convex lens put the flat side as a very large radius. Enter the object distance and the clear aperture, and the tool returns focal length, power in diopters, image distance, magnification, f-number and the Airy disk. The chart shows how the image moves as the object approaches the focal point.

Use catalog radii and the index at your wavelength
Object inside the focal length gives a negative (virtual) image distance
Use a large object distance for collimated or distant sources
Clear aperture is smaller than the mechanical diameter

The equations

The lensmaker equation for a thin lens in air is 1 over f equals (n minus 1) times (1 over R1 minus 1 over R2). The thin lens equation is 1 over f equals 1 over the object distance plus 1 over the image distance. Magnification is minus the image distance divided by the object distance. The f-number is focal length divided by the entrance aperture. The Airy disk diameter to the first minimum is 2.44 times the wavelength times the f-number, which sets the smallest spot a perfect lens can focus a uniformly filled beam to. A Gaussian beam focuses to a different, wavelength and M2 dependent waist.

Worked example

A biconvex N-BK7 lens with R1 of 51.5 mm and R2 of minus 51.5 mm gives a focal length near 49.8 mm, which is a stock 50 mm lens. With a 25.4 mm clear aperture the f-number is about 1.96. At a 633 nm HeNe wavelength the Airy diameter is about 3 um. With the object at 200 mm the image forms near 66 mm behind the lens at roughly 0.33x magnification, inverted. These are the numbers an assembler uses to set the first pass of an alignment jig.

Common mistakes

Sign errors are the main failure: entering both radii as positive turns a biconvex lens into a meniscus and changes focal length dramatically. Using the index at the d-line for a laser at 1064 nm or 10.6 um introduces real error, especially for infrared materials. Treating the thin lens result as the back focal length is wrong for thick lenses. And a diffraction estimate assumes a filled aperture, so a truncated or overfilled Gaussian will not match it.

Frequently Asked Questions

What sign convention does this use?

Light travels left to right. A surface radius is positive if its center of curvature is to the right of the surface. So a biconvex lens has a positive R1 and a negative R2. A flat surface is an infinite radius.

Is this accurate for thick lenses?

It is a thin lens model. For lenses where center thickness is a meaningful fraction of the radius, the effective focal length differs a little and the principal planes shift. Use the vendor data or ray tracing for precision work.

Which index should I use at my laser wavelength?

Use the index from the glass catalog or Sellmeier data at the exact operating wavelength. The values in the list are for the stated reference wavelength. Fused silica, for example, changes by about 0.01 between 1064 nm and the visible.

What is the Airy disk used for?

It is the diffraction limit of a perfect lens with a uniformly filled circular aperture, a lower bound on spot size. It helps judge whether a lens f-number can resolve a feature or reach a spot size before you check aberrations and beam quality.

If optical subassemblies are built and traced through your ERP, Netray can help connect lens specs and measured focal lengths to the part master and lot records. Ask about a private, on-prem setup.

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