Convex Mirror Equation Calculator

Calculator inputs

Enter positive magnitudes only. The calculator applies convex mirror signs internally and shows both magnitude and signed results.

Solve for

Object distance U

Focal length magnitude F

Image distance magnitude V

Object height ho

Distance unit

Decimal places

Graph range multiplier

Example data table

These sample values use positive magnitudes for a convex mirror and assume object height = 3 cm.

Object distance U	Focal length F	Image distance V	Magnification m	Image height hi	Observation
12 cm	6 cm	4.0000 cm	0.3333	1.0000 cm	Virtual, upright, diminished
20 cm	8 cm	5.7143 cm	0.2857	0.8571 cm	Image stays behind mirror
40 cm	10 cm	8.0000 cm	0.2000	0.6000 cm	Smaller image with larger distance
60 cm	15 cm	12.0000 cm	0.2000	0.6000 cm	Convex mirror remains diverging

Formula used

This calculator uses the Cartesian sign convention for mirrors. For a convex mirror, focal length and image distance are negative in signed form.

Signed mirror equation: 1 / f = 1 / do + 1 / di

Convex mirror magnitude form: 1 / V = 1 / U + 1 / F

Image distance magnitude: V = (U × F) / (U + F)

Focal length magnitude: F = (U × V) / (U - V)

Object distance: U = (F × V) / (F - V)

Magnification: m = V / U = hi / ho

Image height: hi = m × ho

Radius of curvature magnitude: R = 2F

Optical power in diopters: P = -1 / f(meters magnitude)

Important note: Because this page accepts positive magnitudes, the displayed signed values help you verify the physics convention directly.

How to use this calculator

Choose what you want to solve: image distance, focal length, or object distance.
Enter the known values as positive magnitudes in the same unit.
Add the object height if you want image height and magnification details.
Pick decimal precision and a graph range multiplier for the Plotly chart.
Click Calculate Now to show the result above the form.
Use the CSV or PDF buttons to export the final report.

Frequently asked questions

1) What does this calculator solve?

It can solve image distance, focal length magnitude, or object distance magnitude. It also reports signed values, magnification, image height, curvature radius, optical power, and mirror-image characteristics.

2) Why are signed values negative for a convex mirror?

Under the standard Cartesian sign convention, a convex mirror has a negative focal length. Its virtual image forms behind the mirror, so image distance is also negative.

3) Can the image distance exceed the focal length?

No. For a real object in front of a convex mirror, the virtual image distance magnitude stays smaller than the focal length magnitude and the object distance.

4) Why is the image always upright?

Magnification for a convex mirror is positive because the image is virtual and upright. Its magnitude remains below one, so the image is diminished.

5) Can I calculate focal length from image distance?

Yes. Choose the focal-length mode or object-distance mode. Enter the other known values as positive magnitudes, and the calculator reconstructs the full convex-mirror solution set.

6) Does the selected unit change the physics?

No, as long as every distance uses the same unit. The calculator converts units internally for optical power, then reports results using your selected unit.

7) How is optical power computed?

Optical power equals 1 divided by focal length in meters, with the convex mirror carrying a negative sign. The result is reported in diopters.

8) Can I use this page for concave mirrors?

No. Concave mirrors can produce real or virtual images and use different sign outcomes. This page is tuned specifically for convex-mirror cases.