Mirror Equation Calculator
The mirror equation 1/f = 1/do + 1/di governs image formation by spherical mirrors. For a concave mirror (positive f), objects beyond the focal point form real inverted images. For a convex mirror (negative f), all images are virtual and upright. The focal length of a spherical mirror equals half its radius of curvature: f = R/2. The lateral magnification is m = -di/do, with the same interpretation as for lenses: negative means inverted, positive means upright. Use this calculator to solve for focal length, image distance, or object distance given the other two. Distances are measured from the mirror surface along the optical axis.
Mirror equation
1/f = 1/do + 1/di
f = R / 2 (R = radius of curvature)
m = -di / do
Sign convention (real-is-positive): in front of mirror is positive for both object and image distances. Concave f is positive, convex f is negative.
Mirror types and typical applications
- Concave mirrors: makeup mirrors, dental mirrors, reflecting telescopes, solar concentrators, satellite dish antennae.
- Convex mirrors: car side mirrors (wide field of view), security surveillance mirrors, convex driving mirrors at blind corners.
- Plane mirrors: flat f (f = infinity), di = -do, m = +1. Image is virtual, upright, same size.
- Parabolic mirrors: eliminate spherical aberration for on-axis beams; used in precision telescopes and laser resonators.
Mirror equation: frequently asked questions
What is the mirror equation?
The mirror equation is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance from the mirror surface, and di is the image distance. For spherical mirrors, f = R/2, where R is the radius of curvature. This equation is identical in form to the thin-lens equation but uses a different sign convention.
What sign conventions apply to mirrors?
For the standard sign convention (real-is-positive for mirrors): object distance do is positive if the object is in front of the mirror (real object). Image distance di is positive for real images in front of the mirror and negative for virtual images behind the mirror. Focal length f is positive for concave (converging) mirrors and negative for convex (diverging) mirrors.
What is the difference between concave and convex mirrors?
A concave mirror curves inward (like the inside of a bowl) and has a positive focal length. It can form real inverted images when the object is beyond the focal point, or virtual upright magnified images when the object is between the focal point and the mirror. A convex mirror curves outward (like the back of a spoon) and always forms virtual, upright, reduced images regardless of object position.
How does mirror magnification relate to image orientation?
Lateral magnification m = -di/do. A negative m means the image is inverted (real image from concave mirror with object beyond f). A positive m means the image is upright (virtual image). |m| > 1 means the image is larger than the object; |m| < 1 means it is smaller.
Why do car side mirrors say 'objects in mirror are closer than they appear'?
Car side mirrors are convex (diverging) mirrors with negative focal length. They produce virtual, reduced images of objects behind, which makes objects appear farther away than they actually are. The wider field of view is the advantage; the reduced apparent size is the trade-off that the warning label addresses.
Official sources
- OpenStax University Physics Volume 3, Chapter 2: Geometric Optics. openstax.org.
- NIST, Physical Measurement Laboratory. physics.nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.