Curved mirrors

Hold a shiny spoon up close and your face grins back, huge and upright. Turn the spoon around and the same face shrinks to a tiny, distant dot. Nothing about your face changed — only the curve of the surface reflecting it did. A plane mirror always gives one dull answer: same size, same way up, flipped left-right. A curved mirror is far more interesting, because the direction its surface bends decides whether light rays are pulled together or pushed apart, and that single choice controls everything about the image — its size, its orientation, and whether you could actually catch it on a screen. This article covers the two spherical mirror types tested in ICSE Class 8: concave and convex, how each treats parallel light, and how to predict the image each one produces.

The core insight

A concave mirror curves inward and converges light, giving images that change with object distance, while a convex mirror curves outward and always diverges light into a single fixed type of image — virtual, upright and diminished.

The core idea

A spherical mirror is simply a small, curved patch cut from the surface of a hollow sphere, silvered on one side to reflect. Depending on which side is silvered, it behaves in one of two opposite ways.

Concave mirror — the reflecting surface curves inward, like the inside of a bowl or the inside of a spoon. Every point on the surface tilts slightly toward a common central point in front of the mirror, so parallel rays of light striking it are bent inward and brought together (converged) at that point.
Convex mirror — the reflecting surface curves outward, like the back of a spoon or the outside of a shiny ball. Every point on the surface tilts slightly away from the middle, so parallel rays striking it are bent outward and spread apart (diverged), appearing to come from a point behind the mirror.

Two fixed points describe every spherical mirror. The centre of curvature ( $C$ ) is the centre of the sphere the mirror was cut from, and the focus ( $F$ ) is the single point where a concave mirror actually converges parallel rays (or the point a convex mirror's diverged rays appear to spread from). These two points sit on the same straight line through the middle of the mirror, and the focus is always the midpoint between the mirror's surface and the centre of curvature:

f = \frac{R}{2}

where: $f$ is the focal length (distance from the mirror to the focus $F$ ) and $R$ is the radius of curvature (distance from the mirror to the centre $C$ ). At this level, treat $f = R/2$ purely as a stated fact for locating the focus roughly midway along the mirror's axis — no problem here asks you to compute $f$ or $R$ through several algebraic steps; that level of calculation, along with the full mirror formula, is Class 9 work.

Figure

Parallel rays entering a concave mirror bend inward and meet at the focus, while parallel rays entering a convex mirror bend outward as if spreading from a point behind the mirror

Why it works

The behaviour of each mirror follows directly from a simple rule: light reflects off any surface so that the incoming and outgoing rays make equal angles with the surface at that point (the same reflection law as a plane mirror), but on a curved mirror this "tilt" of the surface changes continuously from point to point. On a concave mirror, every point on the bowl-shaped surface is angled slightly toward the central axis. A ray coming in parallel to the axis hits a point that is tilted inward, so it is reflected inward too — and because of the mirror's spherical shape, all such rays cross at the same point, the focus. This is why a concave mirror can genuinely gather and concentrate light. What image forms depends on how far the object sits from the mirror. An object placed very close to the mirror (nearer than the focus) has its reflected rays still diverging when they leave the mirror, so they never actually meet in front of the mirror — they only appear to meet when traced backward behind it, giving a virtual image that is upright and magnified. An object placed farther away (beyond the focus) has its reflected rays genuinely converging and crossing in front of the mirror, so they form a real image — one that could be caught on a screen — which comes out inverted, and is diminished, same-size, or magnified depending on exactly how far the object is. On a convex mirror, every point on the surface is angled slightly away from the central axis, so a parallel ray is always bent outward, away from its neighbours, no matter where it strikes. The reflected rays therefore never converge in front of the mirror for any object position — they only spread apart, appearing to originate from the focus behind the mirror. Because this outward-bending happens the same way for every object distance, a convex mirror always produces exactly one kind of image: virtual, upright, and diminished. This consistency, plus the fact that a curved-outward surface "sees" a wider slice of the scene than a flat mirror of the same size, is exactly why convex mirrors are chosen wherever a wide, predictable field of view matters more than image size.

Worked example

A student holds a shiny steel spoon and looks at their own reflection, first in the concave (inner, bowl) side held very close to the face, then in the convex (outer, back) side held at the same distance.

Step 1. Identify each surface. The inner, hollowed side of the spoon curves inward, so it is a concave (converging) mirror. The outer, rounded back of the spoon curves outward, so it is a convex (diverging) mirror.

Step 2. Analyse the concave side. The face is held very close to the spoon — much nearer than the mirror's focus. As explained above, an object closer than the focus of a concave mirror produces reflected rays that only appear to meet behind the mirror, so the image is virtual, and at this close distance it is magnified and upright. This is exactly why the concave inside of a spoon (like a shaving or makeup mirror) shows a large, right-way-up face.

Step 3. Analyse the convex side. A convex mirror gives the same type of image regardless of distance: virtual, upright and diminished. So the same face, viewed in the outer back of the spoon, appears small and shrunk, though still upright and the right way round.

Answer: the concave (inner) side shows a magnified, upright, virtual image of the face, while the convex (outer) side shows a diminished, upright, virtual image of the same face — one spoon, two completely different pictures, purely because of which way the surface curves.

Competitive stretch

A torch or car headlight places its bulb near the focus of a concave reflector rather than close to the mirror. With the source at the focus, rays leaving the bulb strike the mirror and reflect back parallel to the axis — the reverse of parallel rays converging to the focus. This produces a strong, roughly parallel beam instead of light scattering in all directions, which is why headlight and torch reflectors are always concave, never convex.

Common traps

Assuming every mirror behaves like a plane mirror (always same-size, upright, virtual) — curved mirrors change image size and orientation depending on both mirror type and object distance.
Mixing up the names — remember concave curves inward, like the inside of a cave, and converges light; convex curves outward and diverges light.
Believing a convex mirror can ever magnify or invert an image — it cannot; a convex mirror gives a virtual, upright, diminished image for every object position, with no exceptions.
Treating $f = R/2$ as something to calculate through a multi-step numerical problem — at this level it is a stated relationship for locating the focus, not an exam calculation.

Ask the tutor: Curious why a torch reflector uses a concave mirror instead of a convex one, or want to trace more ray diagrams for different object distances? Ask the AI tutor to walk through it with you.

Why does my face look magnified in the concave side of a spoon but tiny in the convex side?

It comes down to which way the surface curves relative to the focus. Your face is much closer to the spoon than the focus of the concave side, so that side's converging surface reflects rays that only seem to meet behind the mirror, producing a large, upright virtual image. The convex back of the spoon always diverges light no matter how close you stand, so it always produces a small, upright virtual image. Same face, same distance, opposite curvature, opposite result.

If f = R/2, why can't I use it to calculate the focal length in a numbers problem?

You certainly could in principle, but at Class 8 level the syllabus only asks you to know and state the relationship, not to plug in values and solve multi-step problems with it. Numerical questions that combine $f$ , $R$ , object distance and image distance using the full mirror formula belong to Class 9 and above. For now, treat $f = R/2$ as a fact you can quote to explain roughly where the focus sits, not as a formula to calculate with.

Why don't we use a concave mirror for a car's rear-view mirror instead of convex, since concave mirrors can magnify?

A concave mirror only magnifies when the object is closer than its focus, and traffic behind a car is usually much farther away than that, so a concave mirror would actually show real, inverted images for distant vehicles — confusing and unsafe. A convex mirror avoids this entirely: it gives a consistent, upright, diminished view at every distance and captures a wider slice of the road because its surface curves away on all sides. Predictability and wide coverage matter more than magnification for checking traffic, which is why convex wins here.