Formula used
Mirror equation: 1/f = 1/u + 1/v
- u is the object distance (real object in front is positive).
- v is the image distance (real image in front is positive, virtual is negative).
- f is the focal length (concave positive, convex negative).
Magnification: m = -v/u
Radius relation: R = 2f
How to use this calculator
- Select what you want to solve from the dropdown.
- Choose mirror type: concave or convex.
- Pick your unit system (cm, m, mm, in, ft).
- Enter the required positive magnitudes for the shown fields.
- Press Calculate to view results above the form.
- Use the CSV or PDF buttons to export your report.
Example data table
| Mirror | U (cm) | F (cm) | Computed V (cm) | m | Image |
|---|---|---|---|---|---|
| Concave | 30 | 15 | 30 | -1.000 | Real, inverted, same size |
| Concave | 40 | 15 | 24 | -0.600 | Real, inverted, diminished |
| Concave | 20 | 15 | 60 | -3.000 | Real, inverted, enlarged |
| Convex | 30 | 15 | -10 | 0.333 | Virtual, upright, diminished |
| Convex | 50 | 20 | -14.286 | 0.286 | Virtual, upright, diminished |
Mirror point guide
1) What “mirror point” means
The “mirror point” is the computed image position along the principal axis. This page links object distance (U), image distance (V), and focal length (F) using the mirror equation. Pick one unknown and the calculator returns a consistent value plus an interpretation.
2) Real and virtual image data
The sign of V is meaningful. V > 0 indicates a real image in front of the mirror that can be projected on a screen. V < 0 indicates a virtual image behind the mirror, visible only by viewing the mirror. The result card labels nature and orientation.
3) Concave vs convex numbers
Concave mirrors use positive focal length and may produce real images when the object lies beyond the focal point. Convex mirrors use negative focal length and always yield an upright, diminished virtual image. For instance, with U = 30 cm and F = 15 cm (convex), V is about −10 cm.
4) Focal point edge case
If U equals F, the term (1/F − 1/U) becomes zero, so V has no finite value. Optically, reflected rays leave parallel and the image forms at infinity. The calculator detects this condition and reports it clearly for lab alignment and homework checks.
5) Magnification and size change
Magnification is computed by m = −V/U. The magnitude |m| indicates size change: values above 1 are enlarged, below 1 are diminished, and near 1 are same size. In the example, U = 20 cm and F = 15 cm gives V = 60 cm and m = −3.
6) Radius of curvature relation
Spherical mirrors satisfy R = 2F. That lets you move between radius and focal length without extra measurements. If a mirror is labeled R = 40 cm, the focal length magnitude is 20 cm. If you enter F = 15 cm (concave), the radius magnitude is 30 cm.
7) Unit conversion and precision
You may work in mm, cm, m, inches, or feet. The calculator converts internally to meters, then returns results in your chosen unit. For most problems, 2–4 decimals are enough; for measured data comparisons, 6 decimals help. Exports keep the displayed rounding for records.
8) Practical measurement tips
Measure distances from the mirror’s vertex along the axis. Enter U and other inputs as positive magnitudes, then let the tool assign signs based on mirror type and the computed image position. Keep a note of unit choice, U, and mirror type. Exported PDF reports support quick sharing.
FAQs
1) Why does my V come out negative?
A negative V means the image is virtual and located behind the mirror. This occurs for convex mirrors, and also for concave mirrors when the object is closer than the focal length.
2) Do I enter negative focal length for a convex mirror?
No. Enter the focal length magnitude as a positive number. Select “convex” and the calculator applies the negative sign internally, then shows signed and magnitude values.
3) What if I only know the radius of curvature?
Select “Focal length (F) from R” and enter R as a magnitude. The tool uses F = R/2 and applies the correct sign from the mirror type selection.
4) Why does it say the image is at infinity?
If U equals F, then 1/F − 1/U becomes zero, so V is not finite. Physically, reflected rays are parallel, so no finite screen position captures the image.
5) How is magnification interpreted?
m = −V/U. The minus sign indicates inversion for real images. The size factor is |m|: above 1 is larger, below 1 is smaller, near 1 is same size.
6) Which distances should I measure in an experiment?
Measure U from the mirror’s vertex to the object along the principal axis. For a real image, measure V from the vertex to the screen where the image is sharpest.
7) Can this calculator be used for lenses?
This tool is designed for mirrors and includes the radius relation R = 2F. Thin lenses use a related equation but different sign conventions, and they do not use mirror radius directly.