Curved Mirrors
P, F, C — the anatomy of a spherical mirror
What this lesson covers
Why it matters
A spoon is two mirrors in one: the bowl shows you upside-down, the back shows you tiny and upright. Before we explain either, three points on an axis need names.
The idea in plain words
The vocabulary of curvature. Tap the terms.
f = R/2
A concave mirror has R = 40 cm. Where is its focus?
20 cm from the pole, on the axis
- on the glass: P (pole) — the geometric centre of the mirror's own surface
- off the glass: C (centre of curvature) — centre of the sphere the mirror was cut from; R = PC is its radius
- the working point: F (focus) — where parallel paraxial rays meet (concave) or seem to diverge from (convex) — midpoint of PC
- the two spoons: concave vs convex — reflecting on the INside (converging) vs the OUTside (diverging)
- f = R/2 = 40/2
Predict first
The focus F of a spherical mirror sits…
The mirror is a slice of a sphere centred at C. Paraxial rays parallel to the axis converge at the midpoint of PC: the focus, with f = R/2.
- exactly halfway between the pole P and centre of curvature C (f = R/2) — correct
- at the centre of curvature
- on the mirror's surface
What you do
Pin the three landmarks in order — P on the glass, F at the midpoint, C at the sphere's heart.
Check yourself
A convex mirror's focus is virtual because…
Diverging rays traced backwards meet behind the glass — same idea as the concave lens's F.
Focal length 15 cm means the radius of curvature is…
R = 2f — the relation runs both ways.
The inside of a polished spoon acts as a…
The bowl curves TOWARD you: concave — hence your upside-down breakfast reflection.
- reflected rays only APPEAR to come from it (behind the mirror) — correct
- it doesn't exist
- convex mirrors have no focus
- 30 cm — correct
- 7.5 cm
- 15 cm
- concave mirror — correct
- convex mirror
- plane mirror