Mirror Equation Calculator – Spherical Mirror Formula
Calculate focal length, object distance, or image distance for spherical mirrors. Our calculator works for both concave and convex mirrors.
1/f = 1/u + 1/v (f = R/2 for spherical mirrors)
Mirror Equation
f = focal length, u = object distance, v = image distance
Choose what to solve for
Select focal length (f), object distance (u), or image distance (v) from the dropdown.
Enter the known values
Fill in the two known quantities. Use positive values for real objects and negative for virtual.
Calculate and interpret results
The calculator shows the unknown value and magnification. Negative image distance means virtual image.
| Quantity | Concave Mirror | Convex Mirror |
|---|---|---|
| Focal length (f) | Positive (+) | Negative (−) |
| Object distance (u) | Always positive (+) | Always positive (+) |
| Image distance (v) | + for real, − for virtual | Always negative (−) |
| Magnification (m) | − for inverted, + for upright | Always positive (+) |
Note: All distances are measured from the pole (center) of the mirror along the principal axis.
Concave Mirror (Converging)
| Object Position | Image Type | Orientation | Size |
|---|---|---|---|
| Beyond C (2f) | Real | Inverted | Diminished |
| At C (2f) | Real | Inverted | Same size |
| Between C and F | Real | Inverted | Magnified |
| At F | At infinity | — | — |
| Between F and pole | Virtual | Upright | Magnified |
Convex Mirror (Diverging)
Convex mirrors always produce virtual, upright, diminished images regardless of object position. This is why they're used in rearview mirrors and security applications—they provide a wide field of view.
What's the difference between concave and convex mirrors?
Concave mirrors curve inward (like a cave) and converge light rays. They can form real or virtual images. Convex mirrors curve outward and diverge light rays. They always form virtual, upright, diminished images.
When is an image real vs virtual?
Real images form where light rays actually converge—they can be projected on a screen. Virtual images appear where rays seem to come from—they can't be projected. For mirrors: positive v = real, negative v = virtual.
What does magnification tell me?
Magnification (m) = image height / object height = -v/u. If |m| > 1, the image is magnified. If |m| < 1, it's diminished. Negative m means inverted image; positive means upright.
How is focal length related to radius of curvature?
For spherical mirrors: f = R/2. The focal length is half the radius of curvature. This relationship holds for both concave and convex mirrors (with appropriate sign conventions).
Why do convex mirrors make things look smaller?
Convex mirrors diverge light rays, making objects appear smaller and farther away than they actually are. This trade-off gives a wider field of view—useful for seeing more area in rearview and security mirrors.
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