About this calculator
Lenses, magnifying glasses, cameras and glasses all follow the thin lens equation: 1 ÷ f = 1 ÷ u + 1 ÷ v, where f is the focal length, u the object distance and v the image distance.
Fill in any two boxes and leave the third empty. Use any one length unit throughout. A converging (convex) lens has a positive f; a diverging (concave) lens a negative f. A negative v means a virtual image.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
f = 10, object at 30
- Image distance (v)
- 15
- Focal length (f)
- 10
- Object distance (u)
- 30
- Magnification
- -0.5×
- Image type
- Real, inverted, smaller
The image is real, inverted and 0.5 times the size of the object.
Show the working
- Thin lens equation: 1 ÷ f = 1 ÷ u + 1 ÷ v (real-is-positive convention: object and real image distances are positive, a virtual image has a negative v, a diverging lens a negative f).
- v = 1 ÷ (1/10 − 1/30) = 15.
- Magnification = −v ÷ u = −15 ÷ 30 = -0.5.
Magnifying glass: f = 10, object at 5
- Image distance (v)
- -10
- Focal length (f)
- 10
- Object distance (u)
- 5
- Magnification
- 2×
- Image type
- Virtual, upright, enlarged
The image is virtual, upright and 2 times the size of the object.
Show the working
- Thin lens equation: 1 ÷ f = 1 ÷ u + 1 ÷ v (real-is-positive convention: object and real image distances are positive, a virtual image has a negative v, a diverging lens a negative f).
- v = 1 ÷ (1/10 − 1/5) = -10.
- Magnification = −v ÷ u = −-10 ÷ 5 = 2.
Find f from u = 30 and v = 15
- Focal length (f)
- 10
- Object distance (u)
- 30
- Image distance (v)
- 15
- Magnification
- -0.5×
- Image type
- Real, inverted, smaller
The image is real, inverted and 0.5 times the size of the object.
Show the working
- Thin lens equation: 1 ÷ f = 1 ÷ u + 1 ÷ v (real-is-positive convention: object and real image distances are positive, a virtual image has a negative v, a diverging lens a negative f).
- f = 1 ÷ (1/30 + 1/15) = 10.
- Magnification = −v ÷ u = −15 ÷ 30 = -0.5.
Sign convention used
- Object distance u is positive for a real object in front of the lens
- Image distance v is positive for a real image (on the far side), negative for a virtual image
- Focal length f is positive for a converging lens, negative for a diverging one
Reading the result
Magnification = −v ÷ u. A negative value means the image is upside down. Above 1 in size it is enlarged, below 1 it is smaller. An object inside the focal length of a converging lens gives an upright, enlarged, virtual image: that is how a magnifying glass works.
Object at the focal point
Place the object exactly at the focal length and the rays leave parallel, so the image forms at infinity. The calculator reports this instead of a number.
Frequently asked questions
What is the thin lens equation?
1/f = 1/u + 1/v, relating focal length, object distance and image distance.
What is a real image?
One that forms where light actually meets, so it can be projected on a screen. A virtual image can only be seen by looking through the lens.
What units should I use?
Any, as long as all three use the same, such as centimetres.
What does a negative magnification mean?
The image is inverted.
Why does it say the image is at infinity?
The object is at the focal point, so the light comes out as parallel rays.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.