Mirror equation
Intermediate
Relates object, image and focal distances.
1/v + 1/u = 1/f1/v + 1/u = 1/f (real-is-positive convention as written here). Magnification m = −v/u.
Concave mirror f = 10 cm with the object 30 cm away: the image forms 15 cm in front of the mirror, real and inverted, m = −0.5.
Set sign convention before plugging in numbers.
In more detail
The mirror equation 1/u + 1/v = 1/f links object distance, image distance and focal length for spherical mirrors, using the sign convention for real and virtual images.
Real-world uses
- Designing telescopes and headlights with mirror equations.
- Predicting image positions for shaving and make-up mirrors.
- Opticians and designers of cameras use the mirror equation to find where an image forms for a given object distance.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What sign convention is used?
Distances are measured from the mirror, with the sign set by whether they are real or virtual.
Why is it useful?
It predicts where images form without drawing ray diagrams.
What is the sign convention?
Distances are measured from the mirror, with real distances positive and virtual distances negative in the usual convention.
Related topics in Optics
Reflection of light · Plane mirrors · Spherical mirrors · Magnification of a mirror · Focal length and radius · Refraction of light