The Mirror Equation
Curved mirrors bend light to form images, just like lenses do. A concave mirror curves inward and can focus light into a real image you could catch on a screen, while a convex or flat mirror always spreads light apart, forming a virtual image that only appears to be behind the mirror.
The formula
1/f = 1/dₒ + 1/dᵢ
- f — focal length (cm): the distance from the mirror to the point where reflected light rays converge
- dₒ — object distance (cm): how far the object sits in front of the mirror
- dᵢ — image distance (cm): how far the image forms from the mirror
Worked example
A concave mirror has a focal length of 10 cm. An object sits 30 cm in front of it. How far from the mirror does the image form?
- f = 10 cm
- dₒ = 30 cm
- 1/dᵢ = 1/f − 1/dₒ
- 1/dᵢ = 1/10 cm − 1/30 cm
dᵢ = 15 cm
Test yourself
The same 10 cm focal length mirror now has an object placed 20 cm away instead of 30 cm. Where does the image form?
- 10 cm
- Correct answer: 20 cm
- 40 cm
Right! 1/dᵢ = 1/10 cm − 1/20 cm = 1/20 cm, so the image forms 20 cm away.
A convex mirror, like the kind used for a car's side mirror, always forms what kind of image?
- Correct answer: Virtual and upright, always smaller than the object
- Real and inverted, always larger than the object
- Real and upright, always the same size
Exactly — convex mirrors always form virtual, upright, shrunk-down images, which is why they can show a wider view.
Where you see this
A car's passenger-side mirror — the one warning objects are closer than they appear — is convex: it trades image size for a wide view. A shaving or makeup mirror is the opposite, concave: your upright, magnified face is a virtual image, and held at the right distance it flips into a real one you could catch on paper.
Common mistakes
The recurring error is forgetting what convex mirrors can and cannot do: they always form virtual, upright, smaller-than-object images — a real image is impossible from one. And the same algebra trap as lenses lives here: image position follows 1/dᵢ = 1/f − 1/dₒ, so a 10 cm focal-length mirror with the object at 20 cm images at 20 cm, and moving the object moves the image.
How it connects
This is the thin-lens equation wearing a mirror: identical 1/f = 1/dₒ + 1/dᵢ, different sign conventions and a different mechanism — reflection instead of refraction. Ray optics ends here; interference and diffraction, next, drop the ray picture entirely and treat light as the wave it is.