Lens and Mirror Equation Calculator

The lens equation and mirror equation are fundamental formulas in geometric optics that relate three quantities: object distance (u), image distance (v), and focal length (f). For lenses, the equation is 1/v − 1/u = 1/f; for mirrors, it is 1/v + 1/u = 1/f — both using the New Cartesian sign convention. The magnification (m) is defined as m = v/u for lenses and m = −v/u for mirrors, and tells you the size and orientation of the image relative to the object. Our lens and mirror equation calculator online implements all four optic types — converging lens, diverging lens, concave mirror, and convex mirror — and automatically applies the correct sign convention so you only need to enter positive magnitudes.

1. Select the Optic Type: Choose from converging lens (convex), diverging lens (concave), concave mirror, or convex mirror. The lens and mirror equation calculator automatically applies the correct sign to the focal length based on your selection — you never need to remember which sign to use.
2. Choose What to Solve For: Select image distance, object distance, or focal length as your unknown. Enter the two known values as positive magnitudes (or as signed values for image distance when solving for object distance or focal length). The lens and mirror equation calculator evaluates the formula in real time.
3. Read the Full Result: The calculator displays the primary result, all four computed quantities (v, u, f, m), and a complete image classification — real or virtual, upright or inverted, and enlarged, diminished, or same size. All calculations run locally in your browser with no data sent to any server.

• Image Distance (v): The signed distance from the lens or mirror to the image. Positive values indicate a real image on the transmission side of a lens or the reflection side of a mirror; negative values indicate a virtual image.
• Magnification (m):The ratio of image height to object height. A positive magnification means the image is upright; negative means inverted. |m| > 1 means enlarged; |m| < 1 means diminished.
• Image Classification: The calculator automatically determines whether the image is real or virtual, upright or inverted, and enlarged or diminished based on the computed magnification and image distance sign.
• Equation Reference: Every result shows the specific formula used and a sign convention summary, making the lens and mirror equation calculator a useful learning tool alongside textbook problems.

This lens and mirror equation calculator uses the New Cartesian sign convention, which is the most widely used convention in modern physics textbooks. Object distance is always taken as negative (object on the left of the optic), and the sign of the focal length is determined by the optic type — the calculator applies this automatically. The calculator assumes thin lens and spherical mirror approximations, which are valid when the lens thickness and mirror curvature are small compared to the object and image distances. For thick lenses or parabolic mirrors, more advanced ray-tracing methods are required.