Curved mirrors form images just like lenses. Concave mirrors are used in telescopes, make-up mirrors and headlights; convex mirrors give a wide field of view in car side mirrors and shop security mirrors.
How to use the Mirror Equation Calculator
- Mirror type
- Object distance d_o
- Mirror given by
- Focal length |f|
- Radius of curvature |R|
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the mirror type and enter the object distance and the focal length (or radius). Positive image distances are real images in front of the mirror; negative ones are virtual, behind it.
Inputs explained
| Field | What to enter |
|---|---|
| Mirror type | Choose one: Concave, Convex, Plane |
| Object distance d_o | Units: cm, mm, m, in, ft |
| Mirror given by | Choose one: Focal length, Radius of curvature |
| Focal length |f| | Units: cm, mm, m, in, ft |
| Radius of curvature |R| | Units: cm, mm, m, in, ft |
What each result means
- Linear magnification = -[Image distance d_i]÷[Object distance d_o]
- Areal magnification = [Linear magnification]^2
Example values
How the main result changes when Object distance d_o changes and everything else stays at the example values above:
| Object distance d_o (cm) | Image distance d_i (cm) |
|---|---|
| 15 | 30 |
| 22.5 | 18 |
| 30 | 15 |
| 37.5 | 13.6364 |
| 45 | 12.8571 |
| 60 | 12 |
Formula
1/d_o + 1/d_i = 1/f, f = R/2, M = −d_i/d_o
Worked example
Inputs — Mirror type: Concave; Object distance d_o: 30 cm; Mirror given by: Focal length; Focal length |f|: 10 cm.
Results — Image distance d_i = 15 cm; Linear magnification = -0.5 ×; Areal magnification = 0.25 ×; Image = Real, inverted.
Key terms
- Focal length
- Half the radius of curvature for a spherical mirror.
Frequently asked questions
Where does a concave mirror form an image of a distant object?
At its focal point.
Why do convex mirrors make things look smaller?
They always form reduced virtual images.
What happens when the object is at the focal point?
No image forms – the reflected rays are parallel.
Is a plane mirror image real?
No – it is virtual, upright and the same size.