Thin Lens Equation Calculator (Focal Length)
Thin lens equation calculator: focal length, object distance or image distance from 1/f = 1/dₒ + 1/dᵢ, with magnification and diopters.
1f = 1do + 1di
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
Use negative image distances for virtual images and negative focal lengths for diverging lenses. Magnification = −dᵢ/dₒ.
Formula
1f = 1do + 1di
| Symbol | Quantity | Units |
|---|---|---|
| do | Object distance | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| di | Image distance (negative = virtual) | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| f | Focal length (negative = diverging) | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
Worked example
Given: do = 30 cm · di = 60 cm
f = do dido + di
Result: f = 20 cm
Focal length (negative = diverging) for different values of Object distance
| do · Object distance | f · Focal length (negative = diverging) |
|---|---|
| 15 cm | 12 cm |
| 22.5 cm | 16.364 cm |
| 27 cm | 18.621 cm |
| 30 cm | 20 cm |
| 33 cm | 21.29 cm |
| 37.5 cm | 23.077 cm |
| 45 cm | 25.714 cm |
| 60 cm | 30 cm |
Other values as in the worked example.
Frequently asked questions
Object at 30 cm, image at 60 cm?
f = 20 cm, magnification −2 (real, inverted, twice as large).
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