Reflection of Light and Spherical Mirrors

We see most things by the light they reflect. This lesson builds up the rule that governs that reflection, applies it to a flat mirror, and then moves to curved (spherical) mirrors and the words used to describe them.

In this lesson you will

State the law of reflection and the idea that light travels in straight lines.
List the four properties of the image formed by a plane mirror.
Tell a concave mirror from a convex mirror by its shape and its reflecting side.
Label the pole, centre of curvature, radius of curvature, principal axis, focus and aperture.
Explain what the principal focus and focal length of a concave mirror mean, and use R = 2f.

Why we can see things

A few objects — the Sun, a flame, a bulb — make their own light. Everything else we see only because light from some source falls on it and bounces off towards our eyes. That bouncing is reflection, and a smooth polished surface like a mirror does it cleanly enough to form an image.

The law of reflection

Light travels in straight lines, so we can draw its path as a ray. When a ray strikes a mirror, draw the normal — a line perpendicular to the surface at that point. Two rules always hold:

The angle of incidence equals the angle of reflection, both measured from the normal.
The incident ray, the reflected ray and the normal all lie in the same plane.

These hold for every mirror, flat or curved.

The image in a plane mirror

Trace two reflected rays from a point on the object back behind the mirror and they meet at the image point. Because no light actually reaches there, the image is virtual. For a plane mirror it is also:

erect (the same way up as the object),
the same size as the object,
as far behind the mirror as the object is in front, and
laterally inverted — left and right are swapped, which is why printed text reads backwards in a mirror.

From a spoon to a spherical mirror

Bend a small piece of a mirrored ball and you get a spherical mirror. If the surface that reflects is the inner, caved-in one, the mirror is concave; if it is the outer, bulging one, it is convex. The shiny spoon in Activity 9.1 is both at once — hollow side concave, back side convex.

The parts of a spherical mirror

Every spherical mirror is described with the same handful of terms. The pole (P) is the middle of the reflecting surface. The centre of curvature (C) is the centre of the sphere the mirror was cut from; the radius of curvature (R) is the distance PC. The line through P and C is the principal axis. The width of the mirror is its aperture, and we assume it is small compared with R so the rules stay simple.

Principal focus and focal length

Send in rays parallel to the principal axis. After reflecting off a concave mirror they cross at one point on the axis — the principal focus (F). After reflecting off a convex mirror they spread apart, but produced backwards they seem to come from a focus behind the mirror. The pole-to-focus distance is the focal length (f), and for a small aperture F sits exactly halfway to C, so R = 2f.

Key terms

Reflection of light: The bouncing back of light into the same medium when it strikes a smooth polished surface such as a mirror.
Normal: The line drawn at right angles to the mirror surface at the point where the ray strikes it. Both angles are measured from this line.
Angle of incidence / angle of reflection: The angle between the incoming ray and the normal, and the angle between the outgoing ray and the normal, respectively.
Spherical mirror: A mirror whose reflecting surface is part of a hollow sphere. If the inner (caved-in) side reflects it is concave; if the outer (bulging) side reflects it is convex.
Pole (P): The centre point of the mirror’s reflecting surface.
Centre of curvature (C): The centre of the sphere the mirror is a piece of. It lies in front of a concave mirror and behind a convex mirror, and is not on the mirror itself.
Radius of curvature (R): The distance from the pole to the centre of curvature (PC).
Principal axis: The straight line through the pole and the centre of curvature. It meets the mirror at right angles at the pole.
Principal focus (F): For a concave mirror, the point on the principal axis where rays arriving parallel to the axis meet after reflection. For a convex mirror, the point behind the mirror from which such rays appear to spread out.
Focal length (f): The distance from the pole to the principal focus (PF).
Aperture: The width of the mirror’s reflecting surface — the part that actually catches light.

Key relationships

Angle of incidence = angle of reflection (measured from the normal).
The incident ray, the reflected ray and the normal all lie in one plane.
A plane-mirror image is the same size as the object and as far behind the mirror as the object is in front.
For a spherical mirror of small aperture, the focus sits halfway between the pole and the centre of curvature: R = 2f.

Formulae

Focus–curvature relation

R = 2f

R = radius of curvature
f = focal length

Magnitudes here; signs are introduced with the mirror formula.

Ray diagrams explained

Reflection at a plane mirror: An incident ray meets the mirror; a normal is drawn at that point; the reflected ray leaves on the other side of the normal making an equal angle with it.
Image in a plane mirror: Two diverging rays from a point on the object reflect off the mirror; produced backwards they meet behind the mirror, locating a virtual image directly opposite and equally far behind.
Parts of a concave mirror: A curved arc for the mirror, its pole P at the centre of the arc, the principal axis running left–right through P, the centre of curvature C and focus F marked on the axis in front of the mirror with F midway between P and C.

Activities

Activity 9.1 — Looking at your reflection in a spoon

What you do: Look at your face in the hollow side of a shiny spoon, then move the spoon slowly away from you. Turn the spoon over and repeat with the bulging side.

What you see: The hollow side gives an image that changes a lot with distance — upright and large when close, then shrinking and flipping as you move away. The bulging side always gives a small upright image.

What it shows: A curved reflecting surface behaves very differently from a flat one, and the two sides of the spoon act as the two kinds of spherical mirror — concave and convex.

Activity 9.2 — Finding the focus of a concave mirror

What you do: Hold a concave mirror facing the Sun and move a sheet of paper in front of it until the bright patch on the paper is as small and sharp as possible.

What you see: At one particular distance the sunlight is gathered to a tiny intense spot; held there, the paper can begin to scorch.

What it shows: Rays coming in parallel to the axis are brought together at the principal focus. The mirror-to-spot distance is the focal length. (In our lesson this is a safe simulation — never look at the real Sun or its reflection.)

What you should be able to do

Recognise

A concave vs a convex mirror from a diagram or description.
The normal, angle of incidence and angle of reflection in a ray diagram.

Explain

Why we can see non-luminous objects.
Why a plane-mirror image is called virtual, and what lateral inversion means.

Draw

A labelled diagram of reflection at a plane mirror.
A concave mirror with P, F, C and the principal axis marked.

State

The two laws of reflection.
The four properties of a plane-mirror image.
Definitions of pole, centre of curvature, radius of curvature, principal focus, focal length and aperture.

Calculate

Focal length from radius of curvature, and vice versa, using R = 2f.

NCERT alignment

This topic corresponds to NCERT Class 10 Science, Chapter “Light — Reflection and Refraction”, sections 9.1, 9.2; activities 9.1, 9.2. Explanations, visuals and worked material here are original.

Quick revision

We see non-luminous objects by light they reflect.
Law of reflection: angle of incidence = angle of reflection; incident ray, normal and reflected ray are coplanar.
Plane-mirror image: virtual, erect, same size, as far behind as the object is in front, laterally inverted.
Concave = inner surface reflects; convex = outer surface reflects.
Parts: pole P, centre of curvature C, radius R = PC, principal axis, principal focus F, focal length f = PF, aperture.
Small aperture: R = 2f (F is midway between P and C).