Thin lens calculator
Image distance, magnification and image type from the thin lens equation.
Fill in the fields and the result will appear here automatically.
Solve the thin-lens equation for a real object with d₀>0. All distances are in centimetres: f>0 for a converging lens, f<0 for a diverging lens; dᵢ>0 for a real image, dᵢ<0 for a virtual image. Magnification sign gives orientation and its magnitude the ratio of linear sizes. At d₀=f there is no finite image distance.
How it works
Formula and logic
1/f = 1/d₀ + 1/dᵢ, magnification −dᵢ/d₀, optical power 100/f in dioptres.
Example
An object 30 cm from a lens with a 10 cm focus forms an image at 15 cm, half the size and inverted.
Fields and units
- What to find — list option
- Focal length — cm
- Object distance — cm
- Image distance — cm
How to use
- — A converging lens takes a positive focal length, a diverging lens a negative one.
- — A positive image distance means a real image on the far side of the lens; a negative one means a virtual image on the same side as the object.
- — Negative magnification means an inverted image, positive means upright; the absolute value is how many times the size changed.
- — The "focal length" mode picks the lens when both distances are already fixed by the layout.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: thin-lens signs and image at infinity
- Limitation
- Paraxial thin lens with the same surrounding medium on both sides. Thickness, aberrations, compound lenses, field of view and a loupe’s angular magnification are excluded. Dioptres here mean reciprocal metres, not spectacle selection or a medical prescription.
FAQ
Why is the magnification negative?
The negative sign denotes inversion: −0.5 means half the linear size. This is the ideal model’s convention, not a description of every compound lens.
What happens when the object sits exactly at the focus?
A converging lens sends rays from a focal-plane point out parallel: the image is described as being at infinity. It cannot be focused on a finite screen. The numerical formula divides by d₀−f=0, so no finite result is returned.
When does a lens act as a magnifying glass?
For a converging lens with 0<d₀<f, the image is virtual, upright and enlarged linearly. A diverging lens and real object also give a virtual upright image, but diminished. This page’s linear ratio is not the angular magnification when viewing through a loupe.
What is optical power in dioptres?
Paraxial thin lens with the same surrounding medium on both sides. Thickness, aberrations, compound lenses, field of view and a loupe’s angular magnification are excluded. Dioptres here mean reciprocal metres, not spectacle selection or a medical prescription.