Physics · Lesson 17

Reflection at plane & curved mirrors

JAMBWAECNECO

What the syllabus asks

JAMB: Reflection of light at plane and curved surfaces

WAEC: Light waves: reflection of light at plane and curved surfaces, laws of reflection, images in plane mirrors, inclined mirrors, rotation of mirrors, concave and convex mirrors, ray diagrams, mirror formula, magnification, uses

NECO: Light waves: reflection of light at plane and curved surfaces, laws of reflection, images in plane mirrors, inclined mirrors, rotation of mirrors, concave and convex mirrors, ray diagrams, mirror formula, magnification, uses

What you will learn

State and apply the laws of reflection.
Describe the image in a plane mirror and solve rotation and inclined-mirror problems.
Define the pole, centre of curvature, focus and focal length of curved mirrors.
Draw ray diagrams for concave and convex mirrors.
Use the mirror formula and magnification with the correct sign convention.
State uses of plane, concave and convex mirrors.

Key points

Laws: i = r; incident ray, reflected ray and normal are coplanar; angles from the normal.
Plane mirror image: virtual, upright, same size, same distance behind, laterally inverted.
Rotating a mirror by θ turns the reflected ray by 2θ; inclined mirrors give n = 360°/θ − 1 images.
Curved mirrors: f = r/2; concave converges, convex diverges.
Concave image depends on object position; virtual only when the object is inside F.
Convex mirror image is always virtual, upright and diminished (wide view).
1/f = 1/u + 1/v; m = v/u; real positive, virtual negative, convex f negative.
Uses: concave for shaving, torches, solar cookers; convex for vehicle and security mirrors.

Start here: The laws of reflection

When light strikes a surface, some or all of it bounces back. This is reflection. A smooth, shiny surface such as a mirror or still water gives regular (specular) reflection: parallel rays stay parallel after reflection, so a clear image forms. A rough surface such as paper or a wall gives diffuse reflection: rays scatter in many directions. That is why you can read a book from any angle but cannot see your face in it.

To describe reflection we draw the normal, a line perpendicular to the surface at the point where the ray strikes. Angles are always measured from the normal, not from the surface.

First law: the incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.
Second law: the angle of incidence equals the angle of reflection (i = r).

These laws apply to every reflecting surface, including curved mirrors, where the normal at any point is the radius drawn through that point.

Worked example 17.1

A ray strikes a plane mirror making 30° with the mirror surface. Find the angle of reflection and the angle between the incident and reflected rays.

The angle with the normal is 90° − 30° = 60°. We convert because the laws use the normal.
Angle of reflection r = i = 60°.
Angle between the rays = i + r = 120°.

60°; 120°

⚠️ Common mistake: giving 30° as the angle of incidence. Always measure from the normal.

Try it yourself. A ray strikes a mirror along the normal. What is the angle of reflection?

Show solution

0°: the ray returns along its own path.

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Practice questions

1. A ray makes 25° with a plane mirror. Find the angle of reflection.

Show worked answer

65°.

2. How many images are formed by two mirrors at 30°?

Show worked answer

11.

3. A mirror is rotated through 12°. Through what angle does the reflected ray turn?

Show worked answer

24°.

4. An object is 40 cm from a concave mirror of focal length 20 cm. Find v.

Show worked answer

1/v = 1/20 − 1/40 = 1/40: v = 40 cm (at C, same size).

5. An object is 12 cm from a convex mirror of focal length 6 cm. Find v.

Show worked answer

1/v = −1/6 − 1/12 = −3/12: v = −4 cm (virtual).

Key words

Incident ray: The ray striking a surface.
Reflected ray: The ray bouncing off the surface.
Normal: A line perpendicular to the surface at the point of incidence.
Real image: An image formed where rays actually meet; it can be caught on a screen.
Virtual image: An image formed where rays only appear to come from; cannot be caught on a screen.
Lateral inversion: Left–right reversal of an image in a plane mirror.
Pole (P): The centre of the surface of a curved mirror.
Centre of curvature (C): The centre of the sphere of which the mirror is part.
Radius of curvature (r): The distance from P to C.
Principal focus (F): The point where rays parallel to the principal axis meet (concave) or appear to diverge from (convex) after reflection.
Focal length (f): The distance PF; f = r/2.
Principal axis: The line through C and P.

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