Mirror Equation Calculator

How it works

1. 1Select the mirror type — concave (converging) or convex (diverging) — to set the sign: f > 0 for concave, f < 0 for convex.
2. 2Enter the focal length magnitude |f| and the object distance dₒ in centimetres. The calculator applies 1/f = 1/dₒ + 1/dᵢ.
3. 3Results show dᵢ in cm, the magnification m = −dᵢ ÷ dₒ, whether the image is real or virtual, and upright or inverted.

Use cases

• Physics students solving spherical-mirror optics problems.
• Engineers designing telescopes, headlights, or dental mirrors.
• Teachers generating worked examples of real vs virtual image formation.

Frequently asked questions

What is the mirror equation?

1/f = 1/dₒ + 1/dᵢ, rearranged dᵢ = (dₒ·f) ÷ (dₒ − f). A concave mirror with f = 10 cm and dₒ = 30 cm gives dᵢ = 300 ÷ 20 = 15 cm — a real image in front of the mirror.

What is the sign convention for mirrors?

Under the real-is-positive convention, a concave (converging) mirror has f > 0 and a convex (diverging) mirror has f < 0. Positive dᵢ means a real image in front of the mirror; negative dᵢ means virtual (behind). m = −dᵢ ÷ dₒ: m > 0 upright, m < 0 inverted.

How is focal length related to the radius of curvature?

For a spherical mirror, f = R ÷ 2. A concave mirror with a 20 cm radius of curvature has a 10 cm focal length, because parallel rays reflect through the focal point midway between the surface and the centre of curvature.