Spherical Mirror Calculator
Where a concave or convex mirror puts the image, how big it is, and whether it is real, virtual, upright or inverted.
Results
What this tool does
A curved mirror obeys the same equation as a thin lens, and the whole of its behaviour comes out of one relationship between three distances. The interesting part is what the signs mean. A concave mirror can enlarge or shrink, invert or not, and produce an image you can catch on paper or one that only appears to exist — all depending on whether the object sits inside or outside the focal point. A convex mirror does exactly one thing, always. Put in the curvature and the object distance and this page tells you which case you are in and what the image looks like.
Formula
1/f = 1/dₒ + 1/dᵢ , f = R ÷ 2 (positive for concave, negative for convex) · m = −dᵢ ÷ dₒ
Variables
| Symbol | Meaning | Unit |
|---|---|---|
kind | Kind of mirror | — |
radius | Radius of curvature | cm |
object_distance | Object distance | cm |
object_height | Object height | cm |
DI | Image distance | cm |
FL | Focal length | cm |
MG | Magnification | x |
HI | Image height | cm |
RL | Can you catch it on a screen? | — |
UP | Is it the right way up? | — |
SZ | Size next to the object | — |
PW | Optical power | 1/cm |
Worked example
- Kind of mirrorconcave
- Radius of curvature40 cm
- Object distance60 cm
- Object height10 cm
- Image distance30.000000 cm
- Focal length20.000000 cm
- Magnification-0.500000 x
- Image height-5.000000 cm
- Can you catch it on a screen?Yes
- Is it the right way up?No
- Size next to the objectSmaller
- Optical power0.050000 1/cm
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
Frequently asked questions
What sign convention does this use?
Distances in front of the mirror are positive. The object is always in front, so its distance is positive. A concave mirror has a positive focal length, a convex one negative. An image distance that comes out positive means a real image, formed in front of the mirror where you could catch it on a card; negative means a virtual image, appearing to sit behind the glass. Magnification is negative when the image is inverted. Textbooks differ on this — some take distances behind as positive — so a book that disagrees with the signs here is not necessarily wrong, and the magnitudes will match either way.
Why is a convex mirror always used for security and reversing?
Because it always gives an upright, reduced, virtual image no matter where the object is — there is no distance at which it flips or blows up, which makes it predictable. Shrinking the image is exactly what squeezes a wide scene into a small mirror, which is why shop corners and car wing mirrors use them. The price is that everything looks further away than it is, which is why those mirrors carry a warning to that effect. A concave mirror does the opposite and changes behaviour depending on whether the object is inside or outside the focal point, which is useful for shaving and useless for traffic.