By Zencalcy Editorial TeamLast reviewed About us
The thin lens equation treats a lens as infinitely thin and relates object distance, image distance and focal length. A converging lens has a positive focal length; a diverging lens has a negative one and forms a virtual image.
Image distance for a converging or diverging lens.
1/f = 1/d_o + 1/d_i
f is the focal length, d_o the object distance and d_i the image distance. Distances on the far side of the lens are positive for a real image.
| Symbol | Meaning |
|---|---|
| f | Focal length; positive converging, negative diverging. |
| d_o | Object distance from the lens. |
| d_i | Image distance; negative means virtual. |
1/d_i = 1/0.1 − 1/0.3 = 6.667, so d_i = 0.15 m. The real image is half the object size and inverted.
Continue with the Angular Dispersion Calculator, Brewster Angle Calculator, or the Camera Exposure Calculator — or browse more optics and light tools and all physics calculators.
A converging lens is thicker at the centre and has positive focal length. A diverging lens is thinner at the centre and has a negative focal length.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Content updated: September 2026