Mirror Equation Calculator

Calculate image distance and magnification for concave, convex, and plane mirrors using the mirror equation 1/f = 1/dₒ + 1/dᵢ. Find image type (real/virtual), radius of curvature, and image height.

Image Distance dᵢ (cm)
—
Magnification m —
Image Type —
Radius of Curvature R (cm) —
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Image Distance dᵢ (cm)
—
Magnification m —
Image Type —
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Image Location

Image Distance dᵢ (cm) —
Image Type —

Size & Magnification

Lateral Magnification m —
Image Height hᵢ (cm) —

Mirror Geometry

Radius of Curvature R = 2f (cm) —

How to Use This Calculator

  1. Select mirror type: Concave (converging), Convex (diverging), or Plane.
  2. Enter focal length as a positive number — the sign is applied automatically.
  3. Enter object distance from the mirror.
  4. Results show image distance, magnification, and image type.
  5. Use specific tabs for each mirror type with detailed breakdowns.

Formula

Mirror Equation: 1/f = 1/dₒ + 1/dᵢ

Radius of Curvature: R = 2f

Magnification: m = −dᵢ/dₒ = hᵢ/hₒ

Concave: f > 0 | Convex: f < 0 | Real image: dᵢ > 0 | Virtual: dᵢ < 0

Example

Example: Concave mirror, f = 15 cm, dₒ = 45 cm. 1/dᵢ = 1/15 − 1/45 = 2/45. dᵢ = 22.5 cm (real, in front). m = −22.5/45 = −0.5 (inverted, half-size).

Frequently Asked Questions

  • 1/f = 1/dₒ + 1/dᵢ, same form as the thin lens equation. For mirrors, f = R/2 where R is the radius of curvature. Concave (converging) mirrors have f > 0; convex (diverging) mirrors have f < 0.
  • Using the standard sign convention: object distance dₒ is always positive (in front of mirror). Image distance dᵢ > 0 means a real image in front of the mirror; dᵢ < 0 means a virtual image behind the mirror. Focal length f > 0 for concave, f < 0 for convex.
  • For a convex mirror, f < 0. Solving 1/dᵢ = 1/f − 1/dₒ always gives dᵢ < 0 for any positive dₒ, meaning the image is always virtual, upright, and diminished. This is why convex mirrors are used as rear-view and security mirrors — wide field of view.
  • A plane mirror is a flat mirror (f → ∞, R → ∞). The image is always virtual, upright, the same size as the object, and located the same distance behind the mirror as the object is in front.
  • Concave (hollow) mirrors converge light and can form real images. Used in telescopes, headlights, shaving mirrors. Convex (bulging) mirrors diverge light, always form virtual diminished images with a wide field of view. Used in rear-view mirrors, store security mirrors.

Related Calculators

👓 Thin Lens Calculator 🔍 Magnification Calculator 🎯 Focal Length Calculator 🔆 Snell's Law Calculator
Sources & References (5) ▾
  1. Mirror Equation — HyperPhysics — Georgia State University
  2. OpenStax University Physics Vol 3, Ch 2.3 — Spherical Mirrors — OpenStax
  3. Hecht, E. Optics (5th ed.) — Pearson
  4. NASA Optics and Photonics Educational Resources — NASA
  5. MIT OCW 8.03 Vibrations and Waves — Mirrors — MIT OpenCourseWare