Thin Lens Equation Calculator
Solve the thin lens equation 1/f = 1/do + 1/di.
Enter any two of focal length, object distance, or image distance to find the third.
Lens optics describes how curved glass surfaces bend light rays to form focused images. The thin lens equation relates focal length, object distance, and image distance, while magnification describes how much larger or smaller the image appears.
Core formulas:
Thin Lens Equation: 1/f = 1/dₒ + 1/dᵢ
Magnification: m = −dᵢ ÷ dₒ = hᵢ ÷ hₒ
Lens Power (Diopters): P = 1 ÷ f (f in meters)
Where:
- f = focal length (positive for converging lenses, negative for diverging)
- dₒ = object distance from the lens (always positive)
- dᵢ = image distance (positive = real image on opposite side; negative = virtual image on same side as object)
- m = magnification (negative = inverted image; |m| > 1 = enlarged; |m| < 1 = reduced)
- hᵢ, hₒ = image and object heights
Lens type summary:
| Lens Type | f sign | Use |
|---|---|---|
| Converging (convex) | + | Cameras, magnifiers, eyes, projectors |
| Diverging (concave) | − | Eyeglasses (nearsighted), beam expanders |
Worked example — camera lens: Object distance dₒ = 2 m, focal length f = 50 mm = 0.05 m. 1/dᵢ = 1/f − 1/dₒ = 1/0.05 − 1/2 = 20 − 0.5 = 19.5 dᵢ = 1 ÷ 19.5 = 0.0513 m = 51.3 mm (image forms just behind the 50mm focal point) Magnification = −0.0513 ÷ 2 = −0.026 (inverted, reduced by 97.4%)
Worked example — magnifying glass: f = 10 cm, object placed at dₒ = 7 cm (inside focal length). 1/dᵢ = 1/10 − 1/7 = 0.1 − 0.143 = −0.043 dᵢ = −23.3 cm (virtual image, upright, on same side as object) m = −(−23.3)/7 = +3.3× magnification