Thin Lens Equation Calculator
Calculate focal length, object distance, or image distance using the thin lens equation.
Supports converging and diverging lenses.
The thin lens equation is one of the most important formulas in optics. It relates three quantities: the focal length of a lens, the distance from the object to the lens, and the distance from the lens to the image.
The formula:
1/f = 1/do + 1/di
Where:
- f = focal length of the lens (in cm or mm)
- do = object distance (distance from the object to the lens)
- di = image distance (distance from the lens to the image)
Rearranged forms:
To find focal length: f = (do × di) / (do + di)
To find image distance: di = (f × do) / (do − f)
To find object distance: do = (f × di) / (di − f)
Sign conventions (standard physics convention):
- Positive focal length = converging lens (convex) — brings light together
- Negative focal length = diverging lens (concave) — spreads light apart
- Positive image distance = real image (formed on the opposite side of the lens from the object)
- Negative image distance = virtual image (formed on the same side as the object)
Magnification tells you how much bigger or smaller the image is compared to the object:
Magnification (M) = −di / do
A magnification greater than 1 means the image is larger than the object. A negative magnification means the image is inverted (upside-down).
Practical applications:
- Camera lenses use this equation to determine focus distance
- Eyeglasses are prescribed based on the focal length needed to correct vision
- Microscopes use multiple thin lenses in series to achieve high magnification
- Projectors calculate the throw distance needed for a desired image size
- Telescopes combine lenses with different focal lengths to magnify distant objects
Common focal lengths:
- Human eye: approximately 17 mm when focused at infinity
- Standard camera lens: 50 mm (considered “normal” for 35mm film / full-frame sensors)
- Magnifying glass: typically 100–300 mm
- Reading glasses (+2.0 diopter): 500 mm focal length
Diopter conversion:
Diopters = 1000 / f (mm) or Diopters = 100 / f (cm)
This calculator lets you solve for any one of the three variables when you know the other two.