Thin Lens Equation Calculator

What is the thin lens equation?

The thin lens equation is 1/f = 1/do + 1/di, with f = lens focal length, do = object-to-lens distance, and di = image-to-lens distance. Linear magnification M = -di/do = hi/ho. This formula applies to thin lenses in the paraxial approximation (rays close

What sign convention does this calculator use?

This calculator uses the real-is-positive convention: object distance do is always positive for real objects; f is positive for converging (convex) lenses and negative for diverging (concave) lenses; positive di means a real image on the opposite side from the object,

How do you read real/virtual, upright/inverted, magnified/diminished images?

Look at the signs of di and M from the calculation: di > 0 means a real image (can be caught on a screen), di < 0 means a virtual image; M > 0 means upright, M < 0 means inverted; |M| > 1 means magnified, |M| < 1 means diminished, and |M| = 1 means

Give a worked example of the thin lens equation.

Example: converging lens f = 10 cm, object at do = 30 cm. Then 1/di = 1/f − 1/do = 1/10 − 1/30 = (3−2)/30 = 2/30 = 1/15, so di = 15 cm. Magnification M = −di/do = −15/30 = −0.5: a real image (positive di, opposite side from object), inverted (negative M)

When does a lens image form at infinity?

The image falls at infinity when the object is exactly at the front focal point (do = f): refracted rays emerge parallel and never meet at a finite distance. The calculator flags this condition explicitly instead of showing misleading numbers.

What kind of image does a diverging lens always produce?

A diverging lens (negative f) always produces a virtual, upright, diminished image for any real object: di is always negative and |M| is always less than 1. This property is used in myopia-correcting lenses (minus glasses) and door peepholes.

What is the difference between the thin lens equation and the lensmaker's equation?

Both are about lenses but at different stages: the lensmaker's equation (calculator #1706 on this site, 1/f = (n−1)(1/R1 − 1/R2)) determines f FROM lens geometry and material (n, R1, R2) — used when designing or making a lens. The thin lens equation assumes

What is the difference between the thin lens equation and the mirror equation?

The formula is the same (1/f = 1/do + 1/di, M = −di/do) but the physics differs: the mirror equation (calculator #1728 on this site) governs light REFLECTION on mirrors, so real images form on the SAME side as the object (in front of the mirror). The lens

What are the three principal rays for a thin lens?

Three principal rays from the object tip: (1) a ray parallel to the principal axis refracts toward the second focal point F2 (converging lens) or spreads as if coming from F2 (diverging lens); (2) a ray through the first focal point F1 emerges parallel to the axis

What is the relationship between focal length and lens power (diopters)?

Lens power P in diopters (D) is the reciprocal of focal length in meters: P = 1/f(m). Example: f = 20 cm = 0.2 m gives P = 5 D (converging); f = −10 cm gives P = −10 D (diverging). The calculator shows diopter power automatically in the results panel every time