Mirror Equation Calculator

The mirror equation is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance — all measured from the pole of the mirror. This formula applies to both concave and convex curved mirrors.

The New Cartesian Sign Convention is standard: distances measured in the direction of incident light are positive, and those against it are negative. For a real object in front of the mirror, u is negative. For a concave mirror, f is negative; for a convex mirror, f is positive.

A plane mirror has a flat surface, meaning its radius of curvature is infinitely large. Since f = R/2, the focal length is also infinite. This means parallel rays reflected by a plane mirror never converge or diverge to a focal point.

Linear (transverse) magnification m = -v/u gives the ratio of image height to object height — a negative value means an inverted image. Areal magnification is the square of linear magnification (m²) and describes how the area of the image compares to the area of the object.

When the object is beyond the center of curvature (C), the image is real, inverted, and diminished. At C, the image is real, inverted, and same size. Between C and focus (F), the image is real, inverted, and magnified. At F, the image forms at infinity. Between F and the pole, the image is virtual, erect, and magnified.

A convex mirror always diverges reflected rays. These diverging rays never actually meet on the same side as the object; they only appear to meet behind the mirror. Therefore, all images formed by a convex mirror are virtual, erect, and diminished, regardless of where the object is placed.

For a spherical mirror, the radius of curvature R is exactly twice the focal length: R = 2f. This relationship comes from the geometry of reflection off a spherical surface, where the center of curvature is twice as far from the pole as the principal focus.

Select your mirror type and choose which variable you want to solve for. Enter the two known values (any two of object distance, image distance, or focal length) and the calculator instantly computes the unknown, along with the radius of curvature, linear magnification, and image characteristics.