Radius and principal axis

The idea

The radius of curvature R is the radius of the mirror's sphere, equal to the distance PC; the principal axis is the straight line through P and C, normal to the mirror at its pole.

A line to the pole

This mirror is part of a sphere. P is its pole and C is the centre of the sphere. Imagine a straight line drawn from C to P.

How does that line meet the mirror's surface at P?

• At right angles, square on to the mirror
• Slanting, at about 45° to the mirror
• Along the surface, just touching the mirror

The stick and the pin

The mirror is tilted. Turn the stick (it pivots on P) until it passes through C, and look at its angle with the mirror. Then slide the pin Q along the mirror and watch the distance CQ.

PC is R

The radius of the sphere of which the reflecting surface of a spherical mirror forms a part is called the radius of curvature, R. The distance PC is equal to R. The straight line passing through the pole and the centre of curvature is called the principal axis. The principal axis is normal to the mirror at its pole.

Normal means at right angles (90°) to the surface.

• What you saw | What it shows
• The stick through P and C made 90° with the mirror at P | The principal axis is normal to the mirror at its pole
• CQ was the same at every spot on the mirror | CQ is a radius of the sphere
• PC and CQ always matched | R = PC

Notes

The radius of curvature R is the radius of the mirror's sphere, equal to the distance PC; the principal axis is the straight line through P and C, normal to the mirror at its pole.

Check yourself

Which line is the principal axis of this concave mirror?

The radius of curvature R of a spherical mirror is equal to …

The edge of a concave mirror is 12 cm from its centre of curvature C. How far is the pole P from C?

Answer: 12 cm

Every point of the mirror is on the same sphere, so every point is the same distance from C. That distance is the radius of curvature. So PC = R = 12 cm.

How does the principal axis meet the mirror at its pole?

• Line 1 — correct. Yes! It passes through both P and C.
• Line 2. Line 2 touches the mirror at P, but it does not pass through C. It lies along the surface.
• Line 3. Line 3 passes through C, but not through the pole P.
• half of the distance PC. R is the whole of PC, not half of it.
• the distance PC — correct. Yes! P is on the mirror and C is the centre of its sphere, so PC is a radius.
• the distance from P to the edge of the mirror. That distance is along the mirror's surface. R is measured from the centre C, not along the mirror.
• At 45° to the mirror. The stick made 90° with the mirror when it lay on the axis.
• Along the surface, touching the mirror. The axis goes through P and C, straight into the mirror. It does not lie along the surface.
• At right angles: it is normal to the mirror at P — correct. Yes! The principal axis is normal to the mirror at its pole.