# Optical Lens Focal Length Calculator (Lensmaker and Thin Lens)

> Source: https://netray.co/tools/optical-lens-focal-length-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Find focal length from surface radii and glass index, then image distance, magnification, f-number and diffraction-limited spot size.

## Category

engineering-plm

## Industry

Photonics and Lasers

## Audience

- Optical engineer
- Laser process engineer
- Optical assembler
- Design engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Lens material

**Key:** n

**Type:** select

**Default:** 1.5168

**Options:**

##### N-BK7 (1.5168 at 587.6 nm)

**Value:** 1.5168

##### Fused silica (1.458 at 587.6 nm)

**Value:** 1.458

##### N-SF11 (1.785 at 587.6 nm)

**Value:** 1.785

##### ZnSe (2.403 at 10.6 um)

**Value:** 2.403

##### Germanium (4.0 at 10.6 um)

**Value:** 4

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

#### Radius of surface 1 (R1)

**Key:** r1

**Type:** number

**Default:** 51.5

**Step:** 0.1

**Unit:** mm

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

#### Radius of surface 2 (R2)

**Key:** r2

**Type:** number

**Default:** -51.5

**Step:** 0.1

**Unit:** mm

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

#### Object distance

**Key:** object_mm

**Type:** number

**Default:** 200

**Min:** 1

**Step:** 5

**Unit:** mm

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

#### Clear aperture diameter

**Key:** aperture_mm

**Type:** number

**Default:** 25.4

**Min:** 0.1

**Step:** 0.1

**Unit:** mm

**Help:** Used for f-number and spot size.

#### Wavelength

**Key:** wavelength_nm

**Type:** number

**Default:** 633

**Min:** 200

**Step:** 1

**Unit:** nm

**Help:** Vacuum wavelength for the diffraction-limited spot estimate.

**Outputs:**

#### Focal length (mm)

**Key:** focal_mm

**Expr:** 1 / ((n - 1) * (1 / r1 - 1 / r2))

**Format:** decimal

**Primary:** true

**Description:** Thin lens lensmaker equation.

#### Optical power (diopters)

**Key:** power_d

**Expr:** 1000 / focal_mm

**Format:** decimal

**Description:** Reciprocal of focal length in meters.

#### Image distance (mm)

**Key:** image_mm

**Expr:** 1 / (1 / focal_mm - 1 / object_mm)

**Format:** decimal

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

#### Magnification

**Key:** mag

**Expr:** -image_mm / object_mm

**Format:** decimal

**Description:** Negative means an inverted real image.

#### f-number

**Key:** fnum

**Expr:** focal_mm / aperture_mm

**Format:** decimal

**Primary:** true

**Description:** Focal length divided by clear aperture.

#### Airy disk diameter (um)

**Key:** airy_um

**Expr:** 2.44 * (wavelength_nm / 1000) * fnum

**Format:** decimal

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

**Chart:**

#### Image distance vs object distance

**Type:** line

**X:** object_mm

**From:** 60

**To:** 600

**Steps:** 30

**Series:**

- image_mm

**Disclaimer:** 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.

## Content

**Intro:** 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.

**Sections:**

#### How to use it

**Body:** 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.

**Bullets:**

- 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

**Body:** 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

**Body:** 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

**Body:** 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.

**Cta:** 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.

**Faq:**

#### What sign convention does this use?

**Answer:** 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?

**Answer:** 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?

**Answer:** 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?

**Answer:** 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.

## Search terms

optical lens focal length calculator, lensmaker equation calculator, thin lens equation calculator, lens focal length from radius of curvature, image distance calculator lens, f number calculator lens, airy disk spot size calculator, lens magnification calculator

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