---
title: "Two-Lens System (Combined Focal) calculator — AperiOptic"
description: "Combined focal length and BFL of two thin lenses separated by d. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/two-lens-system-combined-focal"
---

# Two-Lens System (Combined Focal) calculator

Combined focal length and BFL of two thin lenses separated by d.

Category: [Geometric Optics](https://aperioptic.com/calculators)

Formula: `1/F = 1/f₁ + 1/f₂ − d/(f₁·f₂)`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| f₁ | `f1` | mm | 50 |
| f₂ | `f2` | mm | 100 |
| Separation d | `d` | mm | 20 |

## Result with the default inputs

- Combined F: 38.4615 mm
- Back focal len: 23.0769 mm

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/two-lens-system-combined-focal?f1=50`](https://aperioptic.com/calculators/two-lens-system-combined-focal?f1=50). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Lens, Compound lenses](https://en.wikipedia.org/wiki/Lens#Compound_lenses)

[All optics calculators](https://aperioptic.com/calculators)

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The interactive page: https://aperioptic.com/calculators/two-lens-system-combined-focal (AperiOptic runs in the browser; free, no account). Every page of the site as Markdown: https://aperioptic.com/llms.txt