How to use this calculator
- Enter or choose find.
- The image distance di updates as you type. Use Copy result or Share to keep it.
Method
1/f = 1/do + 1/di; m = −di ÷ do; P (dioptres) = 1 ÷ f (in metres)
- f
- focal length (+ converging, − diverging)
- do
- object distance from the lens
- di
- image distance (+ real, − virtual)
- m
- magnification (negative = inverted)
- P
- optical power in dioptres
Worked example
- 1/di = 1/f − 1/do = 1/10 − 1/30 = 2/30.
- di = 30 ÷ 2 = 15 cm.
- m = −15 ÷ 30 = −0.5, so the image is inverted and half size.
- P = 1 ÷ 0.10 m = 10 D.
An object 30 cm from a 10 cm converging lens forms a real, inverted, half-size image 15 cm behind the lens.
What the result means
A positive image distance means a real image you can project on a screen; a negative one means a virtual image seen by looking through the lens, as with a magnifying glass. All three distances must use the same unit; lens power assumes centimetres.
Assumptions and limits
- Thin lens in air, paraxial (small-angle) rays, real-is-positive sign convention.
- Distances are in centimetres for the dioptre output.
- Thick lenses, lens systems and large-angle rays need principal planes or ray tracing.
- Virtual objects (from a preceding lens) are not handled.
Questions
What if the object is exactly at the focal point?
The rays leave parallel and the image is at infinity, so there is no finite answer.
Which sign convention is this?
Real-is-positive: object distance positive on the incoming side, image distance positive on the far side, converging focal lengths positive.