Lens Magnification Calculator

Linear magnification describes how large an image is compared with the object that produced it. For a thin lens, magnification equals negative image distance divided by object distance. Its absolute value gives the size ratio: a magnitude of two means the image is twice as tall as the object, while a magnitude of one-half means it is half as tall. The sign carries orientation information. A negative magnification indicates an inverted image, and a positive magnification indicates an upright image under the standard Cartesian sign convention. Image height follows directly from magnification multiplied by object height. If a five-centimeter object has a magnification of negative one, its image height is negative five centimeters. The negative sign does not mean a physically negative size; it records that the image is inverted relative to the object. This distinction is important in ray diagrams, cameras, projectors, microscopes, and optical benches. The calculator also applies the thin-lens equation to derive focal length. The reciprocal of focal length equals the reciprocal of object distance plus the reciprocal of image distance, which rearranges to their product divided by their sum. Distances must use one consistent unit. If object and image distances are entered in centimeters, focal length and image height are returned in centimeters. Converting all three inputs to millimeters would preserve magnification and produce millimeter length results. Sign conventions vary among textbooks and engineering disciplines. This tool uses positive object and image distances for the common case of a real object forming a real image on opposite sides of a converging lens, resulting in negative magnification. A virtual image can be represented with a negative image distance, which can produce positive magnification. Before comparing with a class exercise or instrument specification, confirm that it uses the same convention. The thin-lens model assumes an ideal lens whose thickness is negligible relative to object and image distances. Real compound lenses have principal planes, aberrations, finite apertures, distortion, and wavelength-dependent behavior. Photography specifications may use reproduction ratio at the sensor, while telescopes and visual microscopes often quote angular magnification instead of linear magnification. Use this result for basic geometric optics and preliminary design, then use manufacturer data or a full optical model when lens thickness and aberrations matter.