Thin Lens Calculator
Compute image distance, magnification, or lens power for converging and diverging thin lenses. Perfect for optics coursework, camera design, and eyeglass prescription analysis.
About this calculator
The behavior of thin lenses is governed by the thin-lens equation: 1/f = 1/d_o + 1/d_i, where f is the focal length, d_o is the object distance, and d_i is the image distance (all in cm). Rearranging for image distance gives d_i = 1/(1/f − 1/d_o) for a converging lens. Magnification is m = −d_i/d_o; a negative value indicates an inverted image. Lens power in diopters is P = 100/f (when f is in cm), the unit used in optometry prescriptions. Converging (convex) lenses have a positive focal length and can form real or virtual images, while diverging (concave) lenses have a negative focal length and always form virtual, upright, reduced images. The refractive index of the lens material determines focal length via the lensmaker's equation for deeper analysis.
How to use
Suppose you have a converging lens with focal length f = 20 cm and an object placed d_o = 60 cm away. To find image distance: 1/d_i = 1/f − 1/d_o = 1/20 − 1/60 = 3/60 − 1/60 = 2/60, so d_i = 30 cm (a real image on the far side). Magnification: m = −d_i/d_o = −30/60 = −0.5, meaning the image is inverted and half the size of the object. Lens power: P = 100/20 = 5 diopters. Enter your own focal length, object distance, and lens type to instantly calculate any of these values.
Frequently asked questions
How do I calculate the image distance for a diverging lens?
For a diverging lens the focal length is treated as negative. Using the thin-lens equation 1/d_i = 1/f − 1/d_o with a negative f always yields a negative d_i, confirming the image forms on the same side as the object (a virtual image). For example, with f = −15 cm and d_o = 30 cm: 1/d_i = −1/15 − 1/30 = −3/30, giving d_i = −10 cm. The image is virtual, upright, and reduced, which is why diverging lenses are used in peepholes and wide-angle optics.
What does a negative magnification value mean in lens optics?
A negative magnification means the image is inverted relative to the object. The magnitude of magnification tells you the size ratio: |m| > 1 means the image is larger (magnified), while |m| < 1 means it is smaller (reduced). For instance, m = −2 indicates an inverted image twice the height of the object, which is typical of a slide projector or compound microscope objective. Positive magnification always indicates an upright virtual image, as seen through a simple magnifying glass.
When is lens power in diopters used instead of focal length?
Diopters are the standard unit in optometry and ophthalmology because they are additive, making it easy to combine lens powers (e.g., when stacking spectacle and contact lens prescriptions). Power P = 100/f (cm) or P = 1/f (m). A +2.5 D lens has a focal length of 40 cm; a −1.0 D lens corrects mild myopia. Engineers and physicists typically work in focal length for instrument design, while clinicians use diopters for prescriptions. This calculator lets you convert between the two instantly.