Confirming Each Case with a Ray Diagram

Activity 9.3 showed how a concave mirror’s image changes as the object moves. This activity shows why: four simple rules for drawing rays, and the fact that any two of them are enough to locate an image — which you confirm yourself by constructing it.

In this lesson you will

State the four principal-ray construction rules for a concave mirror.
Explain why only two suitable rays, from the same point on the object, are needed to locate an image.
Construct a ray diagram for a new object position and read off the image’s position, size and nature.
Recognise a virtual construction: reflected rays that diverge, located by their backward extensions.

From observation to construction

Activity 9.3 moved a real object in front of a real mirror and watched the image change. That tells you what happens. A ray diagram tells you why — and lets you predict the image for any object position without setting anything up at all.

The four principal-ray rules

Parallel to the axis → reflects through F.
Through F → reflects parallel to the axis.
Through C → strikes the mirror along the normal and retraces its own path.
To the pole P → reflects with the axis as the normal, at an equal angle — the everyday law of reflection.

Why two rays are enough

Countless rays leave every point of the object. After reflecting, every ray that started at the same object point still meets every other one at that point’s image — so any two of the four rules, chosen for convenience, already pin down exactly where that meeting point is. You never need to draw all four.

When the rays never meet

For an object between F and P, the reflected rays spread apart instead of converging. Extended backwards — as dashed lines, never as real light — they meet behind the mirror. That crossing point is a virtual image: erect, enlarged, and impossible to catch on a screen.

Key terms

Principal ray: One of a small set of incident rays from an object, chosen because its reflected path is easy to predict without measuring anything — parallel to the axis, through the focus, through the centre of curvature, or striking the pole.
Backward extension: A dashed line drawn behind a mirror, tracing a diverging reflected ray back to the point it appears to have come from. It is never a real light ray — only where two such extensions cross does a virtual image form.

Key relationships

A ray parallel to the principal axis reflects through the principal focus F.
A ray through F reflects parallel to the principal axis (the reverse of the rule above).
A ray through the centre of curvature C strikes the mirror along the normal and retraces its own path.
A ray striking the pole P reflects with the principal axis as the normal, at an equal angle.
Any two of these rays from the same object point meet — or their backward extensions meet — at the image of that point.

Ray diagrams explained

Ray parallel to the principal axis: Reflects through the principal focus F.
Ray through the principal focus: Reflects back parallel to the principal axis.
Ray through the centre of curvature: Strikes the mirror along its normal and retraces its own path.
Ray to the pole: Reflects with the principal axis as the normal, at an equal angle.
Locating the image: Draw any two of the four rays from the top of the object; where the reflected rays meet (or their backward extensions meet, for a virtual image) is the top of the image.

Activities

Activity 9.4 — Confirming each case with a ray diagram

What you do: For an object beyond C, then between C and F, choose two of the four standard rays from the top of the object and mark where the reflected rays meet. Then try an object between F and P, where the reflected rays spread apart instead.

What you see: The two chosen rays meet exactly where the image forms — matching the position, size and orientation already seen in Activity 9.3. Between F and P, the rays never meet in front of the mirror; only their dashed backward extensions meet, behind it.

What it shows: Two well-chosen rays are enough to predict any image a concave mirror forms — real or virtual — without measuring anything.

What you should be able to do

Recognise

Which construction rule a given ray in a diagram is using.
A virtual construction from its dashed backward extensions.

Explain

Why a ray through the centre of curvature retraces its own path.
Why only two rays are needed to locate an image.

Draw

A complete ray diagram for a concave mirror, for a real and for a virtual image.

State

The four principal-ray construction rules.

Calculate

Left to the “Mirror formula” topic (values, signs and magnification).

NCERT alignment

This topic corresponds to NCERT Class 10 Science, Chapter “Light — Reflection and Refraction”, sections 9.2.1, 9.2.2; activities 9.4. Explanations, visuals and worked material here are original.

Quick revision

Four rules: parallel↔F (reversible pair), through C retraces, pole ray obeys i = r.
Any two rules from the same object point locate that point’s image.
Real image: solid reflected rays actually cross in front of the mirror.
Virtual image: reflected rays diverge; only their dashed backward extensions cross, behind the mirror.
The construction always agrees with what moving a real object showed in Activity 9.3.