What sign convention does this calculator use?

This calculator uses the standard real-is-positive convention: object distances (do) and image distances (di) are positive when they are in front of the mirror (real), and negative when behind it (virtual). Focal length (f) is positive for concave mirrors and negative for convex mirrors.

What is the mirror equation?

The mirror equation is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. It applies to both concave (converging) and convex (diverging) curved mirrors.

How is magnification calculated?

Magnification m = -di / do. A positive value means the image is upright; a negative value means it is inverted. |m| > 1 means the image is enlarged; |m| < 1 means it is diminished.

When is the image real versus virtual?

When di is positive, the image forms in front of the mirror and is real (can be projected on a screen). When di is negative, the image forms behind the mirror and is virtual (cannot be projected).

Does this work for both concave and convex mirrors?

Yes. For concave mirrors use a positive focal length; for convex mirrors use a negative focal length. The equation and this calculator handle both cases.

Mirror Equation Calculator

Name: Mirror Equation Calculator
Availability: InStock
Author: Nham Vu

Solve the mirror equation (1/f = 1/do + 1/di) for any unknown: focal length, object distance, or image distance.

Mirror Equation Solver

1/f = 1/d₀ + 1/dᵢ | m = −dᵢ / d₀

Solve for

Focal Length (f) cm

Positive = concave | Negative = convex

Object Distance (d₀) cm

Usually positive (object in front of mirror)

Image Distance (dᵢ) cm

Positive = real (front) | Negative = virtual (behind)

Enter two known values and click Calculate.

Summary

Solve the mirror equation (1/f = 1/do + 1/di) for any unknown: focal length, object distance, or image distance.

How it works

Select which variable you want to solve for: focal length, object distance, or image distance.
Enter the known values in the input fields using the sign convention (positive = real/in front; negative = virtual/behind).
Click Calculate to apply the mirror equation and see the result.
Review the magnification, image orientation, and image type (real vs. virtual) shown below the result.
Use the concave/convex toggle to auto-apply the correct focal length sign for reference.

Use cases

Solve optics homework problems involving curved mirrors.
Verify lab results for concave or convex mirror experiments.
Determine where an image forms for a given object placement.
Calculate the focal length needed to produce a specific image distance.
Understand image properties (real/virtual, upright/inverted, magnified/diminished).
Prepare for physics exams covering geometric optics.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu