Plan optics problems with clear sign rules. Compute any variable from two entered values quickly. Download a table, verify steps, and compare examples today.
Tip: You can type negative numbers directly. Assisted modes apply typical convex signs only when you enter a magnitude without a sign.
| Convention | f (cm) | dₒ (cm) | Computed dᵢ (cm) | Magnification m | Notes |
|---|---|---|---|---|---|
| Real-positive | -15 | 30 | -10 | 0.3333 | Virtual, upright, reduced image for a convex mirror. |
| Real-positive | -20 | 50 | -14.2857 | 0.2857 | Image appears behind the mirror surface. |
| New Cartesian | +15 | -30 | +10 | 0.3333 | Same geometry, different sign convention. |
The mirror equation relates focal length, object distance, and image distance:
1/f = 1/dₒ + 1/dᵢ
Convex mirrors spread reflected rays outward, so they show a wider field of view than flat or concave mirrors. Because the image is reduced, more scene detail fits inside the same frame. This is why vehicle side mirrors, hallway safety mirrors, and retail security mirrors commonly use convex geometry.
The mirror equation connects focal length f, object distance dₒ, and image distance dᵢ. When you know any two, you can compute the third. In one-unit workflows, keep all distances in the same unit (cm, mm, inches, or meters) before solving.
The calculator uses 1/f = 1/dₒ + 1/dᵢ. Solving rearranges the same relationship, so results should agree if you substitute the output back into the original equation. If the left and right sides differ after rounding, increase decimal places and re-check signs.
Many textbooks treat real objects as positive and virtual images as negative. Under that “real-positive” approach, a convex mirror typically has f < 0 and dᵢ < 0 for a real object. Under the New Cartesian approach, the real object is negative, while convex f and virtual dᵢ are often positive.
For a real object in front of a convex mirror, the image is virtual and upright. In real-positive convention, that usually means dᵢ is negative, and the magnification m is positive. Its size is reduced, so 0 < m < 1 in common cases.
Once f is known, the radius of curvature follows directly: R = 2f. That is useful when you measure a mirror’s curvature mechanically and want the optical focal length. In practical systems, |f| can range from centimeters to meters, depending on how wide the mirror must “see.”
Magnification is computed as m = −dᵢ/dₒ. If you also enter an object height hₒ, the calculator estimates image height with hᵢ = m·hₒ. A positive hᵢ corresponds to an upright image under the chosen sign convention.
The most frequent error is mixing conventions or flipping only one sign. Always choose one sign mode and stick to it for all inputs. Another issue is entering mixed units (cm for one value, inches for another). Finally, if values produce a near-zero denominator, results can become extremely large—this indicates a sensitive setup, not a software bug.
1) What does a negative image distance mean here?
In the real-positive convention, negative dᵢ indicates a virtual image located behind the mirror. The rays appear to diverge from that point, even though light does not actually pass through it.
2) Why is the magnification usually between 0 and 1?
For convex mirrors with real objects, the image is upright and reduced. Under common sign choices, that yields a positive magnification with magnitude less than one, meaning the image height is smaller than the object height.
3) Can I use inches or feet instead of centimeters?
Yes. Select your unit and keep every distance in the same unit. The mirror equation is unit-consistent, so the computed result will match the unit you used for the two known distances.
4) Which sign mode should I pick?
Use the same convention as your textbook or worksheet. If you are unsure, choose “Manual signed input” and enter signs exactly as provided by your source, then compare with the worked example.
5) What is radius of curvature used for?
The radius connects geometry and optics through R = 2f. It helps when you measure mirror curvature or when design specifications list radius rather than focal length.
6) Why did I get an undefined or huge value?
That happens when the computed denominator becomes very close to zero. It indicates your input pair makes 1/f − 1/dₒ (or similar) nearly zero, so the solution becomes extremely sensitive to rounding.
7) Does the calculator handle sign conversion automatically?
In assisted modes, it applies typical convex signs only when you enter a magnitude without a sign. If you type a plus or minus explicitly, the calculator respects exactly what you entered.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.