Lens equation calculator
The thin lens equation covers cameras, projectors, magnifiers and eyes. A negative image distance means a virtual image.
Image distance
52.631 579mm
- Magnification Negative means the image is inverted.
- -0.052 63
- Image height
- 5.263 157 9
- Optical power
- 20.0000 dioptres
- Real image 0 means virtual: on the same side as the object.
- 1
Show the working
- Focal length = 50
- Object distance = 1000
- Object height = 100
- Image distance = (1000 - 50) != 0 ? 1000 * 50 / (1000 - 50) : 0 = 52.6316
- Magnification = 1000 != 0 ? -52.6316 / 1000 : 0 = -0.052 631 6
- Image height = abs(-0.052 631 6) * 100 = 5.263 16
- Optical power = 50 != 0 ? 1000/50 : 0 = 20
- Real image = 52.6316 > 0 ? 1 : 0 = 1
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
Compare a saved scenario
Recent calculations
The formula
- 1/f = 1/do + 1/di
- magnification = -di/do
- power in dioptres = 1 / f in metres
A negative focal length is a diverging lens and always gives a virtual, upright, reduced image.