Concave Mirror: Image Formation

A concave mirror can shrink a distant view to a point or throw a magnified upright image of something close. Which one you get depends entirely on how far the object sits from the mirror.

In this lesson you will

Predict the position, size, nature and orientation of the image for any object position in front of a concave mirror.
Use the rules for the standard construction rays to locate an image.
Distinguish a real image from a virtual image by where the rays go.
Give everyday uses of concave mirrors and the reason for each.

What a concave mirror does

A concave mirror curves away from you, so it gathers the light it catches towards the axis. Close up it acts like a magnifier; far away it concentrates a scene to a small bright image. The single thing that decides which behaviour you see is the object distance — measured against the two marked points, the focus F and the centre of curvature C.

The six object positions

Working from far to near:

At infinity — a point-sized inverted real image at F.
Beyond C — a diminished inverted real image between F and C.
At C — a same-size inverted real image, also at C.
Between C and F — an enlarged inverted real image beyond C.
At F — reflected rays leave parallel, so no image forms (taken as “at infinity”).
Between F and P — an enlarged erect virtual image behind the mirror.

Notice the trend: as the object approaches F from far away, the real image moves further from the mirror and keeps growing.

Real vs virtual, on this mirror

For five of the six positions the reflected rays genuinely cross in front of the mirror: the image is real and inverted, and a screen placed there would catch it. Only when the object is between F and P do the reflected rays diverge; traced backwards they appear to meet behind the mirror, giving a virtual, erect, enlarged image — the shaving-mirror view.

Drawing the ray diagram

Pick any two of the four standard rays from the top of the object — parallel-then-through-F, through-F-then-parallel, through-C-and-back, or to-the-pole-and-off-at-an-equal-angle. Where the reflected rays meet is the top of the image; drop to the axis for the rest. If they only meet when produced backwards, the image is virtual.

Where concave mirrors are used

Torches, searchlights, vehicle headlamps — the bulb sits at F, so the reflected light leaves as a straight parallel beam.
Shaving and make-up mirrors — the face is kept within F, giving an enlarged erect image.
Dentists’ mirrors — a small enlarged image of the tooth.
Solar furnaces — a large concave dish brings sunlight to an intense focus.

Key terms

Real image: An image formed where reflected rays actually meet. It can be caught on a screen and, for a concave mirror, is always inverted.
Virtual image: An image from which reflected rays only appear to come; the rays never meet. It cannot be caught on a screen and is erect. For a concave mirror this happens only when the object is between F and P.
Magnification (nature): A comparison of image height with object height. Here it is used qualitatively — diminished, same size, or enlarged. The equation comes with the mirror formula.

Key relationships

Object at infinity → tiny inverted real image at F.
Object beyond C → diminished inverted real image between F and C.
Object at C → same-size inverted real image at C.
Object between C and F → enlarged inverted real image beyond C.
Object at F → reflected rays are parallel; no image is formed (image “at infinity”).
Object between F and P → enlarged erect virtual image behind the mirror.
As the object moves from far towards F, the real image moves away from the mirror and grows.

Formulae

Mirror formula (introduced fully in the next topic)

1/v + 1/u = 1/f

u = object distance
v = image distance
f = focal length

New Cartesian signs: distances measured from the pole, object distance negative, concave focal length negative. Covered in “Mirror formula”.

Ray diagrams explained

Ray parallel to the principal axis: A ray coming in parallel to the axis reflects so that it passes through the principal focus F.
Ray through the principal focus: A ray passing through F reflects back parallel to the principal axis.
Ray through the centre of curvature: A ray heading through C strikes the mirror along its normal and retraces its own path.
Ray to the pole: A ray hitting the pole reflects with the principal axis as the normal, making an equal angle on the other side.
Locating the image: Draw any two of these rays from the top of the object; where the reflected rays meet (or appear to meet, produced backwards) is the top of the image.

Activities

Activity 9.3 — Tracking the image as the object moves

What you do: Place a lit candle well beyond C in front of a concave mirror and move a screen until the image is sharp. Repeat with the candle just beyond C, at C, between C and F, at F, and between F and P.

What you see: For most positions a sharp inverted image appears on the screen and its size and distance change in a regular way. At F no image forms on the screen; between F and P no screen image can be caught at all.

What it shows: The image’s position, size and nature are fixed by the object’s position — the pattern summarised in the relationships above.

Activity 9.4 — Confirming each case with a ray diagram

What you do: For each object position, draw two standard rays from the top of the object and mark where the reflected rays meet.

What you see: The drawn image matches the experiment every time — same side, same orientation, same rough size.

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

What you should be able to do

Recognise

The object position from a completed ray diagram, and vice versa.
Whether an image is real or virtual from where the reflected rays go.

Explain

Why the object at F gives no image.
Why the between-F-and-P case gives a virtual, erect, enlarged image.
Why a concave shaving mirror shows an enlarged face but a torch uses one to throw a parallel beam.

Draw

A ray diagram for each of the six object positions.

State

The position, size and nature of the image for every object position (the full table).
The four construction-ray rules for a concave mirror.

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 9.3, 9.4. Explanations, visuals and worked material here are original.

Quick revision

Object position (relative to F and C) fixes image position, size and nature.
Five positions give a real, inverted image; only object-between-F-and-P gives a virtual, erect, enlarged image.
Object at F → no image (reflected rays parallel).
As the object nears F from far away, the real image recedes and enlarges.
Four construction rays; any two locate the image.
Uses: parallel beams (F source), magnified erect views (object within F), solar concentration.