---
title: "Thermal Defocus calculator — AperiOptic"
description: "Focal shift from thermal expansion and dn/dT of the lens material. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/thermal-defocus"
---

# Thermal Defocus calculator

Focal shift from thermal expansion and dn/dT of the lens material.

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

Formula: `f′/f = (1 + α·ΔT)·(n − 1)/(n − 1 + (dn/dT)·ΔT) (≈ 1 + (α − (dn/dT)/(n−1))·ΔT)`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Focal length | `f` | mm | 100 |
| Index n | `n` |  | 1.517 |
| α (CTE) | `alpha` | 10⁻⁶/K | 7.1 |
| dn/dT | `dndT` | 10⁻⁶/K | 3 |
| ΔT | `dT` | K | 20 |

## Result with the default inputs

- Δf: 0.0026 mm
- Δf / f: 25.9428 ppm

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/thermal-defocus?f=100`](https://aperioptic.com/calculators/thermal-defocus?f=100). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Thermal lensing](https://en.wikipedia.org/wiki/Thermal_lensing)

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

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