Lens & Mirror Equation Calculator
Calculate image position, focal length, and magnification for any lens or mirror using the thin lens equation. Covers converging and diverging lenses, concave and convex mirrors.
As an Amazon Associate and CJ Affiliate publisher we earn from qualifying purchases. Prices and availability may vary.
Optics Guide
What should I know about The Thin Lens Equation?
1/f = 1/v + 1/u. Where f = focal length, v = image distance, u = object distance. Sign convention (real-is-positive): real object (in front of lens): u positive. Real image (on opposite side from object): v positive. Virtual image (same side as object): v negative. Converging lens: f positive. Diverging lens: f negative. Lens power: P = 1/f(metres) in dioptres (D). A 25 cm focal length lens: P = 1/0.25 = +4D. Short-sighted (myopia) is corrected with diverging lenses (negative power). Long-sightedness, or hyperopia, is corrected with converging lenses (positive power) instead, since the eye focuses light behind rather than on the retina.
What should I know about Image Characteristics?
To determine image type: real image: rays actually pass through the image point — can be projected on a screen — formed on the opposite side of the lens from the object. Virtual image: rays appear to diverge from the image point — cannot be projected — formed on the same side as the object. Erect vs inverted: m > 0: erect (same way up as object). m < 0: inverted. Magnified vs diminished: |m| > 1: larger than object. |m| < 1: smaller. |m| = 1: same size. For a converging lens: an object placed beyond twice the focal length produces a real, inverted, and diminished image — the configuration used in cameras.
What should I know about Mirror Equation?
Same formula applies to mirrors: 1/f = 1/v + 1/u. Concave (converging) mirror: f = R/2 (where R = radius of curvature), f positive. Convex (diverging) mirror: f negative. Sign convention for mirrors: real object (in front of mirror): u positive. Real image (in front of mirror, same side as object for reflection): v positive. Virtual image (behind mirror): v negative. A concave mirror forms a real, inverted image when the object is beyond the focal point — this is how reflecting telescopes and satellite dishes both work, using a curved mirror to focus incoming light or signals to a single point.
What should I know about Applications?
Camera: converging lens forms a real, inverted image on a sensor. Projector: object (slide/LCD) just beyond f — real, inverted, greatly magnified image on screen. Magnifying glass: object within f — virtual, erect, magnified image. Telescope: objective lens forms real image in focal plane; eyepiece acts as magnifying glass for this intermediate image. Eye: cornea (main converging power ~43D) and crystalline lens (variable 10-20D) form a real, inverted image on the retina. Total eye power is approximately 60 dioptres, combining both the fixed corneal power and the variable lens power the eye adjusts to focus at different distances.