A Thin Lens Equation Calculator
The thin lens equation relates the focal length of a lens to where an object sits and where its image forms. Magnification then tells you how big the image is and whether it is flipped.
Image distance
22.5
- Magnification
- -0.5
- Image height
- -3
- Lens power in dioptres
- 6.6667
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
1/f = 1/do + 1/di, rearranged as di = f x do / (do - f)
- f
- The focal length, positive for a converging lens
- do
- The object distance from the lens
- di
- The image distance from the lens
- m
- The magnification, negative when the image is inverted
How to check the result by hand
- 1
Write down the focal length and the object distance
Use the same units for both. A focal length of 15 and an object distance of 45 both in centimetres is fine; mixing metres and centimetres is the usual source of wrong answers.
- 2
Subtract the focal length from the object distance
45 minus 15 is 30. This difference is the denominator, and it is the number that tells you which side of the focal point the object is on.
- 3
Multiply the focal length by the object distance
15 times 45 is 675. This product goes on top of the fraction.
- 4
Divide to get the image distance
675 divided by 30 is 22.5, so the image forms 22.5 centimetres from the lens, on the far side from the object.
- 5
Work out the magnification
Minus 22.5 divided by 45 is -0.5. The image is half the height of the object and inverted, because the magnification is negative.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate A Thin Lens Equation page.