Thin Lens Calculator
Calculate image distance and magnification using the thin lens equation.
Results
The thin lens equation 1/f = 1/do + 1/di relates focal length, object distance and image distance. Positive focal lengths indicate converging (convex) lenses, negative indicate diverging (concave). This calculator determines where the image forms, how large it is and whether it is real or virtual - essential for camera lens design, eyeglass prescriptions and optical instruments.
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Frequently asked questions
1/di = 1/10 - 1/30 = 2/30, so di = 15 cm. The image is real, inverted and 0.5× magnification (half size). This is how a camera forms images on film.
When do = f, 1/di = 1/f - 1/f = 0, so di = infinity. The rays emerge parallel - no image forms. This is how flashlights and collimators work.
When the object is inside the focal length (do < f). For f = 10 cm and do = 5 cm: 1/di = 1/10 - 1/5 = -1/10, so di = -10 cm. The image is virtual, upright and 2× magnified. This is how a magnifying glass works.
M = -di/do. For di = 15 cm and do = 30 cm, M = -15/30 = -0.5×. Negative means inverted. |M| > 1 means enlarged, |M| < 1 means reduced.
For M = -2 (real, inverted): di = -M × do = 60 cm. Then f = do×di/(do+di) = 30×60/90 = 20 cm focal length.