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Mirror Equation Calculator

Calculate image distance and magnification for a concave or convex mirror using the mirror equation.

Result

Image Distance
30 cm
Magnification
-1x
Image Type
Real, inverted

Uses the mirror equation 1/f = 1/dₒ + 1/dᵢ and magnification m = -dᵢ/dₒ, with the sign convention that a positive image distance means a real image (in front of the mirror) and a negative one means a virtual image (behind the mirror).

About the Mirror Equation

The Mirror Equation Calculator finds where a curved mirror forms an image and how large that image appears, based on the mirror's focal length and the distance of the object in front of it. It handles both concave mirrors (like a shaving or telescope mirror) and convex mirrors (like a car's passenger-side mirror) in a single tool. Students and hobbyists use it to check optics homework or predict image behavior before building a physical setup.

How It Works

Enter the focal length in centimeters, using a positive value for a concave mirror and a negative value for a convex mirror, along with the object distance in front of the mirror. The calculator solves the mirror equation for image distance, then divides that result by the object distance and flips its sign to get magnification. The sign of the image distance determines whether the result is labeled a real, inverted image or a virtual, upright one.

1/f = 1/do + 1/di, rearranged to di = (f x do) / (do - f); magnification m = -di / do

Formula & Methodology

Because the calculator uses the standard mirror sign convention, the object distance is always entered as a positive number, while focal length carries the sign of the mirror type. Once di is found, its sign tells you where the image sits: positive means the image forms in front of the mirror where light rays truly converge (real), negative means it forms behind the mirror's reflecting surface where rays only appear to diverge from (virtual). The magnification's sign then tells you orientation: negative flips the image upside down, positive keeps it right side up, while its magnitude tells you whether the image is larger or smaller than the object.

Examples

Object at the Center of Curvature

For a concave mirror with a 15 cm focal length and an object placed 30 cm away (twice the focal length), the calculator returns an image distance of 30 cm and a magnification of -1. This is a real, inverted image the same size as the object, the classic center-of-curvature case.

Convex Passenger Mirror

With a focal length of -15 cm and an object 20 cm away, the calculator returns an image distance of about -8.57 cm and a magnification of roughly 0.43x. The negative image distance flags a virtual, upright image, smaller than the object, matching how convex mirrors widen the field of view.

Advantages

  • Automatically applies the correct sign convention, so you don't need to memorize whether concave or convex mirrors take a positive or negative focal length.
  • Returns image distance, magnification, and a plain-language image type together, saving a second step of interpreting whether the numeric result means real or virtual.
  • Works for both mirror types with the same two inputs, making it useful for comparing concave and convex behavior side by side.

Common Mistakes

  • Entering a positive focal length for a convex mirror, which produces incorrect results since the sign is what distinguishes the two mirror types in this equation.
  • Mixing up focal length with radius of curvature; for a spherical mirror the radius is twice the focal length, so plugging in radius by mistake doubles the error.
  • Misreading a negative magnification as meaning the image is smaller, when the sign only indicates inversion; the magnitude of the number is what determines size relative to the object.

Edge Cases to Watch For

  • If the object distance is entered as exactly equal to the focal length, the calculator returns an error rather than a result, because do - f becomes zero and the image mathematically forms at infinity.
  • Any convex mirror (negative focal length) will always return a negative image distance no matter what object distance you enter, meaning convex mirrors only ever produce virtual, upright images.
  • For a concave mirror, placing the object closer than the focal length (do less than f) flips the image distance negative too, producing a magnified virtual image, which is how a concave shaving or makeup mirror works.

Common Use Cases

  • Physics and optics students verifying mirror equation homework or lab measurements
  • Photography and telescope hobbyists predicting image size and orientation before assembling curved-mirror optics
  • Instructors generating quick example problems that cover both real and virtual image cases
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

What's the difference between a real and a virtual image?

A real image forms where light rays actually converge and can be projected onto a screen, typically produced by a concave mirror when the object is beyond the focal point, while a virtual image forms where light rays only appear to diverge from (never actually crossing there), can't be projected onto a screen, and is what you see when looking into a convex mirror or a concave mirror with the object closer than the focal point.

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Conclusion

The mirror equation connects a curved mirror's shape to exactly where and how an image will appear, and this calculator handles the sign bookkeeping that trips up most students learning it for the first time. Whether you're checking a concave telescope mirror or a convex safety mirror, the same two inputs and one equation cover both cases.