Thin Lens Calculator

At a glance:The thin-lens equation is the core relation in geometric optics linking focal length, object position and image position: 1/f=1/do+1/di, where f is the focal length (distance at which parallel rays focus), do is the object distance (from object to lens centre) and di is the image distance (from image to lens centre), all in the same length unit (e.g. cm). A 'thin lens' is the idealised model where the lens thickness is negligible compared with f, do and di — accurate for most glasses, magnifiers and camera lenses. Rearranging gives di=1/(1/f−1/do). Example (default): convex lens f=10 cm, object at do=30 cm → 1/di=1/10−1/30=2/30, so di=15 cm. Sign convention (a common Cartesian form): (1) convex (converging, thicker centre) f is positive; concave (diverging, thinner centre) f is negative; (2) object distance do is positive for a real object; (3) image distance di positive → image on the opposite side, a real image projectable onto a screen; di negative → same side as object, a virtual image seen only through the lens. Here di=+15 cm is a real, reduced, inverted image. Common cases: (1) object beyond f (do>f) — convex lens forms a real, inverted image (camera, projector, eye); (2) object inside f (do<f) — convex lens forms a virtual, upright, magnified image (magnifier); (3) concave lens always gives a reduced, upright virtual image (near-sighted glasses). With magnification m=−di/do you also get the image size and orientation. Notes: (1) keep the sign convention; concave f is negative; (2) use the same unit for f, do, di; (3) at do=f the image distance tends to infinity (parallel rays, no image) — this tool returns 0 in that case; (4) f or do of 0 returns 0. A powerful tool for lens imaging, glasses and optical instruments.