Thin Lens Equation Calculator
Image distance, magnification and image height for a thin lens, plus its optical power in dioptres.
Results
Image distance
60.000
mm
Magnification
-0.2000
Image height
12.000
mm
Optical power
20.000
dpt
What this tool does
A negative magnification means the image is inverted, which is what a real image projected on a sensor or screen always is. Use a negative focal length for a diverging lens; when the object sits exactly at the focal point the rays leave parallel and there is no image to find.
Formula
1/f = 1/dₒ + 1/dᵢ ; m = −dᵢ ÷ dₒ
Variables
| Symbol | Meaning | Unit |
|---|---|---|
f | Focal length | mm |
do | Object distance | mm |
ho | Object height | mm |
DI | Image distance | mm |
M | Magnification | — |
HI | Image height | mm |
PW | Optical power | dpt |
Worked example
- Focal length50 mm
- Object distance300 mm
- Object height60 mm
- Image distance60.000 mm
- Magnification-0.2000
- Image height12.000 mm
- Optical power20.000 dpt
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.