Lens equation calculator
With this lens equation calculator you find the image distance, object distance or focal length of a thin lens from two known values, and learn the magnification, image size and image type.
Example: Solve for: Image distance v · Focal length f 10 cm · Object distance u 30 cm · Image distance v 15 cm · Object height 2 cm → Result: v = 15 cm – real image, inverted. Source: Wikipedia – Linsengleichung (Abbildungsgleichung dünner Linsen): 1/f = 1/g + 1/b. Updated: .
How it is calculated
The lens equation is 1/f = 1/u + 1/v. A converging lens with f = 10 cm images an object 30 cm away at 15 cm, inverted and half the size (m = −0.5). In this tool u is the object distance (g) and v the image distance (b).
How it is calculated
The equation holds for thin lenses and rays close to the axis. From two of the three quantities f, u, v the third follows; the magnification is m = h′/h = −v/u. A negative m means an inverted image, a positive m an upright one. Optical power is P = 1/f in dioptres when f is in metres.
Good to know
- If the object is inside the focal length (u < f), the image is virtual, upright and magnified – the principle of the magnifying glass.
- At u = 2f the image is real, inverted and exactly as large as the object (v = 2f).
- Thick lenses and multi-element lenses need principal planes; the thin lens model applies here.
Frequently asked questions
What is the lens equation?
1/f = 1/u + 1/v with focal length f, object distance u and image distance v. For example v = f · u / (u − f).
When is the image virtual?
With a converging lens when the object is inside the focal length (u < f), and with a diverging lens always. The image distance is then negative.
How do you calculate magnification?
m = h′/h = −v/u. With v = 15 cm and u = 30 cm, m = −0.5: the image is half the size and upside down.
How do you convert focal length to dioptres?
P = 1/f with f in metres. A lens with a 10 cm focal length is 10 D.
Sources and legal basis
- Wikipedia – Linsengleichung (Abbildungsgleichung dünner Linsen): 1/f = 1/g + 1/b
- Wikipedia – Thin lens: sign convention and magnification
As of: · Editorial policy
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