Mirror Equation Calculator

The mirror equation relates focal length, object distance, and image distance for spherical mirrors under the paraxial approximation. It is written as one over focal length equals one over object distance plus one over image distance. This calculator rearranges the equation to find image distance from the other two quantities, then calculates lateral magnification as negative image distance divided by object distance. A consistent sign convention is essential. This calculator uses positive object distance for a real object in front of the mirror. A concave mirror has positive focal length because its principal focus lies in front of the reflective surface. A convex mirror has negative focal length because its focus is virtual and lies behind the surface. A positive calculated image distance identifies a real image in front of the mirror, while a negative image distance identifies a virtual image behind it. Magnification describes image size and orientation. Its absolute value is image height divided by object height. A negative magnification indicates an inverted image, and a positive value indicates an upright image. An absolute value above one means enlarged, below one means reduced, and equal to one means unchanged size. Thus image distance and magnification together provide a concise description of where the image forms and how it appears. For a concave mirror, an object beyond the focal point produces a real inverted image. Moving the object toward the focal point sends that image farther away and increases its magnitude. At exactly the focal point, reflected rays are parallel and the ideal image is at infinity, so the calculator reports that singular condition rather than dividing by zero. An object between a concave mirror and its focus produces an upright, enlarged virtual image. A convex mirror produces an upright, reduced virtual image for every positive real-object distance. Distances may technically use any one consistent length unit because the equation is homogeneous. The interface labels centimetres for convenient laboratory and classroom values. If metres or millimetres are preferred, use that same unit for both inputs and interpret image distance in the same unit; magnification remains dimensionless. Focal length is half the radius of curvature for an ideal spherical mirror. The equation assumes rays close to the principal axis and a mirror whose aperture is small relative to its radius of curvature. Wide-angle rays can produce spherical aberration, and real optical systems may include aspheric surfaces, multiple elements, alignment errors, and finite aperture effects. Use ray tracing or optical design software for precision systems. For introductory optics, lab preparation, and rapid sign-convention checks, this mirror equation calculator provides a clear numerical result and physical classification.