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)
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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
- Select mirror type: Concave (converging), Convex (diverging), or Plane.
- Enter focal length as a positive number — the sign is applied automatically.
- Enter object distance from the mirror.
- Results show image distance, magnification, and image type.
- 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.
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Sources & References (5) ▾
- Mirror Equation — HyperPhysics — Georgia State University
- OpenStax University Physics Vol 3, Ch 2.3 — Spherical Mirrors — OpenStax
- Hecht, E. Optics (5th ed.) — Pearson
- NASA Optics and Photonics Educational Resources — NASA
- MIT OCW 8.03 Vibrations and Waves — Mirrors — MIT OpenCourseWare