Mirror Equation Calculator
The mirror equation relates the focal length of a curved mirror to the object distance and image distance: 1/f = 1/d_o + 1/d_i. This fundamental formula in geometric optics lets you predict where an image forms, how large it is, and whether it is real or virtual, upright or inverted.
The mirror equation 1/f = 1/do + 1/di applies to both concave and convex mirrors using the sign convention: distances are positive in front of the mirror and negative behind it. A concave mirror has a positive focal length and can produce both real and virtual images, while a convex mirror has a negative focal length and always produces virtual, upright, reduced images.
The magnification m = -di/do tells you the image size relative to the object. When |m| > 1 the image is enlarged; when |m| < 1 it is diminished. A negative magnification means the image is inverted.
Curved mirrors are used everywhere: concave mirrors focus light in telescopes, headlights, and solar furnaces; convex mirrors provide a wide field of view in vehicle side mirrors and security mirrors. Understanding the mirror equation is key to designing any optical system involving curved reflective surfaces.