Calculator Inputs
Formula Used
The mirror formula in Cartesian sign convention is:
1 / f = 1 / v + 1 / u
Where:
- f = focal length
- u = object distance
- v = image distance
Rearranged forms used by this calculator:
v = (f × u) / (u − f)u = (f × v) / (v − f)f = (u × v) / (u + v)m = −v / ufor magnificationhᵢ = m × hₒfor image heightR = 2ffor radius of curvatureP = 1 / f(m)for mirror power in diopters
Use signed distances consistently. The result depends on the sign convention you follow during entry.
How to Use This Calculator
- Select what you want to calculate: object distance, image distance, or focal length.
- Choose the mirror type and the unit you want to work in.
- Enter known signed values using Cartesian sign convention.
- Optionally enter object height to compute image height.
- Pick your preferred decimal precision.
- Press the calculate button to show results above the form.
- Review magnification, image nature, orientation, and graph behavior.
- Use CSV or PDF export to save the generated output.
Example Data Table
| Case | Mirror | u (cm) | f (cm) | v (cm) | Magnification | Image Type |
|---|---|---|---|---|---|---|
| 1 | Concave | -45 | -15 | -22.5 | -0.5 | Real, inverted, diminished |
| 2 | Concave | -22.5 | -15 | -45 | -2 | Real, inverted, magnified |
| 3 | Concave | -10 | -15 | 30 | 3 | Virtual, erect, magnified |
| 4 | Convex | -30 | 15 | 10 | 0.3333 | Virtual, erect, diminished |
These examples use Cartesian signs. Negative values usually indicate points in front of the mirror for incident light from the left.
Frequently Asked Questions
1. What does the mirror formula calculate?
It relates object distance, image distance, and focal length for spherical mirrors. When two values are known, the third can be calculated directly.
2. Why are some distances negative?
This calculator uses Cartesian sign convention. Distances measured in front of the mirror are commonly negative, while distances behind the mirror are positive.
3. How is magnification determined?
Magnification is calculated with m = -v/u. Its sign shows orientation, and its absolute value shows whether the image is enlarged or reduced.
4. What does a positive image distance mean?
A positive image distance usually indicates a virtual image formed behind the mirror. Virtual images are generally erect in this sign convention.
5. Can this calculator handle convex mirrors?
Yes. Convex mirrors are supported. Under Cartesian sign convention, their focal length is typically positive, and they often produce virtual, erect, diminished images.
6. Why is the result undefined at focus?
When the object is at the focal point of a concave mirror, reflected rays become parallel. The image forms at infinity, so finite image distance cannot be reported.
7. What is mirror power in diopters?
Mirror power is the reciprocal of focal length measured in meters. It gives another way to compare optical strength using a standard lens-style unit.
8. Why should I enter object height?
Object height is optional, but it allows the calculator to estimate image height. That makes it easier to study size change and orientation together.