Mirrors that are not flat
A scooter's headlamp throws one long, even beam. A curved mirror behind the bulb helps.
The steps below name the parts of a curved mirror. The table after them says what each part is.
- The axis runs through the mirror's pole.
- Pole P, centre C and focus F sit on it.
- C is the radius R from P. It is the centre of the sphere.
- F sits halfway: R = 2f.
Loading lab…
The rule
A mirror cut from a hollow sphere is a spherical mirror. A concave mirror curves inwards, like the inside of a spoon. A convex mirror curves outwards, like the back of a spoon.
In this lesson f and R are plain lengths, with no signs. For a small spherical mirror, f = R/2. Small means the mirror is narrow compared with R.
| Name | What it is |
|---|---|
| Pole (P) | The middle point of the mirror's face. |
| Centre of curvature (C) | The centre of the sphere the mirror is cut from. |
| Radius of curvature (R) | The distance from P to C. |
| Principal axis | The straight line through P and C. |
| Principal focus (F) | The point where rays parallel to the axis meet after reflection. |
| Focal length (f) | The distance from P to F. It is half of R. |
Worked example
A concave mirror has R = 30 cm. Then f = 30 ÷ 2 = 15 cm.
A classroom can check f without a formula. Point a concave mirror at a far window. A far window sends nearly parallel rays. Move a paper screen until the image of the window is sharp. The distance from mirror to screen is about f. Never do this with the Sun.
Rays from a bulb at F leave the mirror parallel. That is why a headlamp makes a long beam.