Thin Lens Equation Calculator — Focal Length, Object & Image Distance1/f = 1/d₀ + 1/dᵢ · m = −dᵢ/d₀ · Convex · Concave · Magnification
Use this free Thin Lens Equation Calculator to instantly solve any unknown variable in the standard thin lens formula of geometric optics:
1/f = 1/d₀ + 1/dᵢ
f = focal length (m or cm) | d₀ = object distance from lens | dᵢ = image distance from lens | m = −dᵢ/d₀ = linear magnification
Enter any two known optical values to automatically solve the third — computing: focal length (f) in metres or centimetres · object distance (d₀) from the optical centre · image distance (dᵢ) — positive (real) or negative (virtual) · linear magnification (m = −dᵢ/d₀) · image nature — real/virtual, upright/inverted, enlarged/diminished — for both convex (converging) lenses (positive f) and concave (diverging) lenses (negative f).
This online optics calculator is trusted across all levels of physics and optical engineering: A-Level, GCSE, AP Physics, IB Physics, JEE, and NEET optics and lens problems, ray diagram analysis — principal focus, centre of curvature, and image formation, camera lens and photography focal length calculations, eyeglass and contact lens prescription power (dioptre = 1/f) calculation, telescope and microscope objective lens magnification analysis, and projector and optical instrument design. Sign conventions follow the standard Cartesian sign convention — distances measured from the optical centre with real distances positive and virtual distances negative — under the paraxial (small angle) approximation.
All calculations use the thin lens formula (1/f = 1/d₀ + 1/dᵢ) under the paraxial approximation — assuming thin lenses, small angles, and negligible lens thickness. Lens power in dioptres (D) = 1/f (metres).
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Optics Calculator — Focal Length, Snell's Law, and Lens Magnification
The thin lens equation 1/f = 1/do + 1/di relates focal length f, object distance do, and image distance di. A converging lens with f = 10 cm and an object at 30 cm forms an image at di = 15 cm on the far side — real, inverted, and magnified by 0.5×. Moving the object inside the focal length produces a virtual, upright, magnified image (magnifying glass). The optics calculator applies the thin lens equation to compute image position and magnification for any combination of focal length and object distance, distinguishing real from virtual images.
Snell's Law (n₁sinθ₁ = n₂sinθ₂) governs refraction at interfaces between optical media. Light traveling from air (n=1.0) into glass (n=1.5) at 30° bends to 19.47° inside the glass — toward the normal because it is entering a denser medium. Total internal reflection occurs when light tries to exit a denser medium at an angle exceeding the critical angle (41.8° for glass-to-air). Fiber optics exploit total internal reflection to transmit light with minimal loss over kilometers. The calculator computes refraction angles and identifies the critical angle for any pair of materials.
Camera optics use the same thin lens equation to determine depth of field, hyperfocal distance, and exposure. A 50mm lens on a 35mm camera focused at 3 meters has depth of field from 2.4 m to 4.0 m at f/4, but from 1.6 m to infinity at f/11. The relationship between aperture, depth of field, and diffraction limits determines the sharpest possible aperture for a given focal length. The calculator covers the photography-specific application of lens equations with sensor size, aperture, and focus distance as inputs.