Thin Lens Equation

Also known as lens formula · 1/f = 1/do + 1/di · lensmaker's relation

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Worked example: d_o = 30 cm, d_i = 15 cm → f = 10 cm — press Try an example to run it live, then adjust anything.

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Grade 10Grade 10 Science

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Thin Lens Equation explained

The thin lens equation is the workhorse of geometric optics, tying together where the object sits, where its image forms, and the lens's focal length. The sign conventions carry the physics: a positive $d_i$ is a real image on the far side of a converging lens, a negative $d_i$ a virtual image on the near side. Place an object exactly at the focal point and $1/d_i$ must vanish — the image recedes to infinity, which is how a magnifying glass produces parallel rays.

A camera focused on a subject 2 m away with a 50 mm lens forms its image at $d_i = (1/0.05 - 1/2)^{-1} \approx 51.3$ mm behind the glass — the millimeter of travel that the focus ring provides.

Thin Lens Equation

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Where

$f$ = Focal length (m)
$d_o$ = Object distance (m)
$d_i$ = Image distance (m)

Missing one of these? Work it out first, then come back

Focal length — Focal Length of a Spherical Mirror, Lens Power in Diopters
Object distance — Lens Magnification (m = −d_i/d_o), Speed, Distance & Time
Image distance — Lens Magnification (m = −d_i/d_o), Speed, Distance & Time

Part of this formula set

Lens and mirror equations

5 formulasThe thin lens and mirror equations with the two magnification relations and lens power — everything needed to place an image and say how big it is.