Pole and centre of curvature
A mirror has two middles: one on the mirror and one out in space.
The ball behind the mirror
A concave mirror is a small piece of a big ball. Imagine the whole ball it was cut from.
Where is the centre of that ball?
What this lesson covers
The idea
The pole P is the centre of a spherical mirror's reflecting surface; the centre of curvature C is the centre of the sphere it forms part of, lying in front of a concave and behind a convex mirror.
The ball behind the mirror
A concave mirror is a small piece of a big ball. Imagine the whole ball it was cut from.
Where is the centre of that ball?
- In the air, in front of the mirror
- On the mirror, at the middle of its surface
- Behind the mirror, inside its steel back
Find the two middles
First pin the pole: the middle of the mirror's surface. Then use a compass: drag its point until the dotted circle fits the mirror. Try the concave and the convex mirror.
P is on it, C is not
The centre of the reflecting surface of a spherical mirror is a point called the pole, P. It lies on the surface of the mirror. The reflecting surface is part of a sphere, and the centre of that sphere is the centre of curvature, C. It is not a part of the mirror: it lies outside its reflecting surface. C lies in front of a concave mirror and behind a convex mirror.
The shiny side is the front. The shaded side is the back.
- Point | Concave mirror | Convex mirror
- Pole P | On the mirror, at the middle of its surface | On the mirror, at the middle of its surface
- Centre of curvature C | In front of the mirror | Behind the mirror
Notes
The pole P is the centre of a spherical mirror's reflecting surface; the centre of curvature C is the centre of the sphere it forms part of, lying in front of a concave and behind a convex mirror.
Check yourself
Which point is the pole of this concave mirror?
The dotted circle is the sphere that this convex mirror is part of. Which point is its centre of curvature?
Where does the centre of curvature C lie?
Which statement about the centre of curvature C is right?
- Point X. X is at the edge of the mirror. The pole is at the middle of its surface.
- Point Y — correct. Yes! The pole is the centre of the reflecting surface, on the mirror.
- Point Z. Z is the centre of the sphere, in front of the mirror. That is C, not the pole.
- Point X. X is on the mirror: it is the pole. The centre of curvature is the centre of the sphere.
- Neither: a mirror has no such point. Every spherical mirror is part of a sphere, and a sphere has a centre. That is C.
- Point Y — correct. Yes! It is the centre of the sphere, and it lies behind a convex mirror.
- In front of a concave mirror and behind a convex mirror — correct. Yes! It is on the shiny side for a concave mirror, and on the back side for a convex one.
- Behind a concave mirror and in front of a convex mirror. It is the other way round. For a concave mirror C is on the shiny side, in front.
- On the surface of every mirror, at its middle. The middle of the surface is the pole P. C is the centre of the sphere, outside the mirror.
- C is the middle point of the mirror's surface. The middle point of the surface is the pole, P. C is the centre of the sphere.
- C is not a part of the mirror: it lies outside its reflecting surface — correct. Yes! C is only a point in space, the centre of the sphere.
- C lies on the mirror, next to the pole. The mirror is a thin piece of the sphere's surface, so the sphere's centre is far from it, not on it.