What is the Mirror Equation?
The mirror equation (also called the mirror formula) connects the object distance u, image distance v, and focal length f of a curved or plane mirror:
1/f = 1/v + 1/u
Types of Mirrors
- Concave mirror — curved inward; focal length f > 0. Can form both real (inverted) and virtual (erect) images depending on object position.
- Convex mirror — curved outward; focal length f < 0. Always forms a virtual, erect, and diminished image.
- Plane mirror — flat surface; focal length f = ∞. Image is always virtual, erect, same size, and located at the same distance behind the mirror as the object is in front.
Sign Convention
This calculator uses the real-is-positive sign convention:
- Object distance (u) — positive for a real object placed in front of the mirror.
- Image distance (v) — positive if the image forms in front of the mirror (real image); negative if the image forms behind the mirror (virtual image).
- Focal length (f) — positive for concave mirrors, negative for convex mirrors.
Radius of Curvature
The radius of curvature R is related to the focal length by:
R = 2f
Magnification
The mirror equation calculator also computes two types of magnification:
- Linear magnification (m) — the ratio of image height to object height: m = −v/u. A negative value means the image is inverted.
- Areal magnification (m²) — the ratio of image area to object area. Always positive.
Magnification interpretation:
- |m| > 1 → image is enlarged
- |m| < 1 → image is diminished
- |m| = 1 → image is the same size
How to Use This Calculator
- Select the mirror type: Concave, Convex, or Plane.
- Choose your unit of distance (metric: mm, cm, m; or imperial: in, ft).
- Select which variable you want to calculate (f, v, or u).
- Enter the two known values.
- Click Calculate to see the result, magnification, and image type.
Concave Mirror — Example
An object is placed 30 cm in front of a concave mirror with focal length f = 20 cm. Find the image distance:
1/v = 1/f − 1/u = 1/20 − 1/30 = 3/60 − 2/60 = 1/60
v = 60 cm (real, inverted image)
Linear magnification: m = −v/u = −60/30 = −2 (inverted, enlarged 2×)
Convex Mirror — Example
An object is placed 20 cm in front of a convex mirror with focal length f = −15 cm:
1/v = 1/f − 1/u = 1/(−15) − 1/20 = −4/60 − 3/60 = −7/60
v ≈ −8.57 cm (virtual, erect image behind mirror)
Plane Mirror
For a plane mirror, f = ∞, so the equation simplifies to v = −u. An object 25 cm in front of the mirror forms a virtual image 25 cm behind it. Magnification m = 1 (same size, erect).
FAQs
What is the difference between concave and convex mirrors?
Concave mirrors curve inward (like the inside of a spoon) and can form real or virtual images depending on object position. Convex mirrors curve outward and always produce virtual, diminished, upright images.
Why is the image in a convex mirror always virtual?
Because the focal point of a convex mirror is behind the mirror surface (f < 0). The reflected rays diverge and only appear to meet behind the mirror, forming a virtual image.
Can a plane mirror form a real image?
No. A plane mirror always forms a virtual image located at the same distance behind the mirror as the object is in front. The image cannot be projected onto a screen.
What does negative magnification mean?
A negative magnification (m < 0) means the image is inverted relative to the object. This occurs when a real image is formed by a concave mirror.