A plane mirror (Reflection and Plane Mirrors) keeps rays spreading exactly as they were. A curved mirror bends their paths. A concave mirror, curved in like a cave or a spoon's bowl, gathers rays that arrive parallel to its axis to one point, the focal point $F$. A convex mirror, bulging out, spreads them as if they came from a focal point behind it. For a spherical mirror, $f = R/2$, half the radius of curvature.
Key idea
Three principal rays from the tip of the object find the image: (1) a ray parallel to the axis reflects through $F$; (2) a ray through $F$ reflects parallel to the axis; (3) a ray through the center of curvature $C$ reflects straight back. Where the reflected rays meet is a real image; where they only seem to come from is a virtual image.
Why it works
Each principal ray follows from the law of reflection. A ray through $C$ hits the mirror along a radius, which is the normal there, so it reflects straight back. The parallel ray and the ray through $F$ are each other's paths run backward: light paths work in both directions.
| Object (concave mirror) | Image |
|---|---|
| beyond $C$ | real, inverted, smaller, between $F$ and $C$ |
| at $C$ | real, inverted, same size, at $C$ |
| between $C$ and $F$ | real, inverted, larger, beyond $C$ |
| at $F$ | no image: the rays leave parallel |
| inside $F$ | virtual, upright, larger, behind the mirror |
Common mistake
Thinking that covering half of a mirror removes half of the image. Every point of the object sends rays to every part of the mirror, so the uncovered half still forms the whole image, just dimmer. Check: the principal rays are only the easy ones to draw; countless other rays build the same image.
Worked example: Object beyond C
An object stands $30\ \text{cm}$ from a concave mirror with $f = 10\ \text{cm}$. Describe the image.
- $C$ is at $2f = 20\ \text{cm}$, so the object is beyond $C$.
- The parallel ray reflects through $F$; the ray through $F$ comes back parallel; they cross between $F$ and $C$, below the axis.
- The image is real, inverted and smaller. (The mirror equation, next, puts it at $15\ \text{cm}$.)
Answer: Real, inverted, smaller, between F and C
Worked example: A makeup mirror
Why does a concave makeup mirror make your face look bigger and upright when you are close to it?
- Close to the mirror, your face is inside $F$.
- The reflected rays spread apart, so they never meet in front of the mirror. Traced backward, they meet behind it.
- That gives a virtual, upright, enlarged image.
Answer: Object inside F: virtual, upright, larger