Convex Mirror: Image Formation and Uses
Turn a spherical mirror so the bulging side faces you and everything changes: the focus moves behind the glass, and no matter where the object is, the image is small, upright and virtual. That predictability is exactly why vehicles use convex mirrors.
In this lesson you will
- Explain why the centre of curvature and focus of a convex mirror lie behind it.
- Describe how parallel rays reflect from a convex mirror and why its focus is virtual.
- State the position, size and nature of the image for any object in front of a convex mirror.
- Explain why a convex mirror gives a wider field of view than a plane or concave mirror.
- Give the main uses of convex and concave mirrors with a reason for each.
Flip the curve outward
A concave mirror caves inward and gathers light. Turn the same piece of sphere around so the bulging side reflects and you have a convex mirror. It does the opposite job: it spreads a parallel beam apart, which is why it is also called a diverging mirror.
The centre and focus move behind the mirror
The mirror is still a slice of a sphere, but now it is the outside of that sphere. The sphere’s centre — the centre of curvature C — is therefore behind the reflecting surface. The principal focus F still sits halfway between the pole and C, so it is behind the mirror too. The relationship R = 2f is unchanged.
Why the focus is virtual
Send in rays parallel to the principal axis. Each obeys the law of reflection, and the reflected rays spread apart — they never cross in front of the mirror. Extend them straight backward, though, and the extensions all meet at one point behind the mirror. That point is the focus. Since no light actually reaches it, and the rays only appear to come from it, the focus of a convex mirror is virtual.
The image: always the same kind
Take any object in front of a convex mirror and build the image with two rays — one parallel to the axis (reflects as if from F), one aimed at C (reflects back on itself). The reflected rays diverge; only their backward extensions cross, behind the mirror. So the image is:
- behind the mirror, between the pole and F;
- virtual (it cannot be caught on a screen);
- erect; and
- diminished.
Move the object farther away and the image shrinks and slides towards F. Bring it closer and the image grows — but it never reaches the object’s size and never leaves the pole-to-F gap. When the object is at infinity the image is a point at F. These are the two rows of the convex-mirror image table.
A wider field of view
Because a convex mirror spreads reflected rays outward, an observer at a fixed spot can see a much wider stretch of the scene in it than in a plane or concave mirror of the same size. The image is smaller, but there is far more of it.
Uses of convex mirrors
The image is always upright and shrunk, and the field of view is wide — ideal when one small mirror must survey a large area:
- Rear-view and wing mirrors on vehicles — the driver sees an upright, compact view of a wide band of the road behind.
- Safety mirrors at blind corners, in shops and on staircases.
Uses of concave mirrors
For completeness, the inward-curving mirror earns its keep by either producing a parallel beam or a magnified upright image:
- Torches, searchlights, headlamps — a bulb at the focus sends light out as a near-parallel beam.
- Shaving and make-up mirrors — the face, kept within the focal length, appears enlarged and upright.
- Dentists’ mirrors — a small enlarged, upright view of a tooth.
- Solar furnaces — a large dish concentrates near-parallel sunlight at its focus.
Concave vs convex — the comparison to keep
| Concave | Convex | |
|---|---|---|
| Effect on light | converges | diverges |
| Focus | in front (real) | behind (virtual) |
| Image | depends on object position; real or virtual | always virtual, erect, diminished |
| Field of view | narrow | wide |
Key terms
- Convex mirror
- A spherical mirror whose reflecting surface is the outward-bulging side. It spreads a parallel beam apart, so it is also called a diverging mirror.
- Centre of curvature (convex)
- The centre of the sphere the mirror belongs to. For a convex mirror it lies behind the reflecting surface.
- Principal focus of a convex mirror
- The point behind the mirror from which reflected rays appear to diverge when the incident rays are parallel to the principal axis. Because no light actually passes through it, this focus is virtual.
- Field of view
- The extent of the scene an observer can see in the mirror from a fixed position. A convex mirror gives a wider field of view than a plane or concave mirror of the same size.
Key relationships
- For a convex mirror the centre of curvature C and the focus F are behind the mirror.
- F lies halfway between the pole and C (small aperture): the R = 2f relationship still holds.
- Parallel incident rays reflect so that they diverge; their backward extensions meet at F.
- Any object in front → image between P and F, behind the mirror, virtual, erect, diminished.
- As the object moves farther away, the image shrinks and moves towards F.
- Object at infinity → point-sized image at F, virtual and erect.
Formulae
Focus–curvature relation (unchanged)
R = 2f
- R = radius of curvature
- f = focal length
Magnitudes here. Signed values, and the mirror formula, are covered in the next topic.
Ray diagrams explained
- Parallel ray
- A ray parallel to the principal axis reflects so that it appears to come from the focus F behind the mirror.
- Ray aimed at the centre of curvature
- A ray directed towards C behind the mirror strikes the surface along its normal and reflects straight back along itself.
- Locating the image
- Draw these two rays from the top of the object. The reflected rays diverge; their backward extensions cross behind the mirror, and that crossing point is the top of the (virtual) image.
Activities
Activity 9.5 — Moving a pencil in front of a convex mirror
What you do: Stand a pencil upright in front of a convex mirror and watch its image as you move the pencil towards and away from the mirror.
What you see: The image is always upright, always behind the mirror, and always smaller than the pencil. Moving the pencil away makes the image shrink and slide towards the focus; bringing it closer makes the image grow but it never reaches full size.
What it shows: A convex mirror forms one kind of image for every object position — virtual, erect and diminished, between the pole and the focus.
Activity 9.6 — Comparing the field of view
What you do: From one fixed spot, look at the same wide scene in a plane mirror, then a concave mirror, then a convex mirror of the same size.
What you see: The convex mirror shows the largest stretch of the scene; the concave mirror shows the least.
What it shows: A convex mirror has the widest field of view, which is why it is used where one small mirror must watch a large area.
What you should be able to do
Recognise
- A convex mirror and its diverging effect on a parallel beam.
- That C and F of a convex mirror are behind the mirror.
Explain
- Why the focus of a convex mirror is called virtual.
- Why the image in a convex mirror is always virtual, erect and diminished.
- Why convex mirrors are used as rear-view / wing mirrors.
Draw
- A ray diagram for an object in front of a convex mirror (two rays + backward extensions).
- The ray diagram for an object at infinity (image as a point at F).
State
- The two rows of the convex-mirror image table (finite object; object at infinity).
- The uses of convex mirrors and of concave mirrors, with a reason for each.
Calculate
- Left to the “Mirror formula” topic.
NCERT alignment
This topic corresponds to NCERT Class 10 Science, Chapter “Light — Reflection and Refraction”, sections 9.2; activities 9.5, 9.6. Explanations, visuals and worked material here are original.
Quick revision
- Convex = diverging mirror; C and F are behind it; R = 2f still holds.
- Parallel rays reflect and diverge; backward extensions meet at the virtual focus F.
- Any object in front → image between P and F, behind, virtual, erect, diminished.
- Farther object → smaller image, closer to F. Object at infinity → point image at F.
- Convex mirror = widest field of view → rear-view / wing / safety mirrors.
- Concave uses: parallel beams (torch, headlamp, solar furnace) and magnified erect images (shaving, dentist).