One Side of a Steel Spoon Turns You Upside Down
Learn to label the pole, centre of curvature, principal axis and focus of a spherical mirror, draw ray diagrams for a concave mirror at every object position, and explain why a convex mirror always gives a small erect image.
Why does a steel spoon show two completely different images?
Look into the hollow side of a steel spoon held at arm's length and your face appears upside down. Turn it over and the bulging side shows you upright but tiny.
The metal is the same. Only the curvature has reversed — and curvature decides where the reflected rays meet.
The hollow side is a concave mirror and gathers rays together; the bulging side is a convex mirror and spreads them apart. That single difference produces every result in this page, which covers the second part of the ICSE Class 8 Physics chapter on light: the parts of a spherical mirror, ray diagrams, and what each mirror is used for.
The metal is the same. Only the curvature has reversed — and curvature decides where the reflected rays meet.
The hollow side is a concave mirror and gathers rays together; the bulging side is a convex mirror and spreads them apart. That single difference produces every result in this page, which covers the second part of the ICSE Class 8 Physics chapter on light: the parts of a spherical mirror, ray diagrams, and what each mirror is used for.
Formula
What are the pole, centre of curvature and focus of a mirror?
A spherical mirror is a piece cut from a hollow sphere, silvered on one side. Five terms locate everything on it.
- **Pole () — the centre of the reflecting surface, the middle of the mirror itself.
- Centre of curvature () — the centre of the sphere the mirror was cut from. For a concave mirror it lies in front of the mirror; for a convex mirror, behind it.
- Radius of curvature ()** — the distance , the radius of that sphere.
- Principal axis — the straight line through and , meeting the mirror at right angles.
- **Principal focus () — the point on the principal axis where rays parallel to the axis meet after reflection (concave), or from which they appear** to diverge (convex). The distance is the **focal length ().
The relation between them:**
The focus sits exactly halfway between the pole and the centre of curvature.
Worked example. A concave mirror is cut from a sphere of radius . Then
so is in front of the pole and is in front of it.
And in reverse: a mirror of focal length has
Why concave mirrors are called converging. Parallel rays actually cross at , so the light really does arrive there and a real image can be caught on a screen. A convex mirror spreads the rays, so they never cross and is only a point they seem to come from — making every convex image virtual.
- **Pole () — the centre of the reflecting surface, the middle of the mirror itself.
- Centre of curvature () — the centre of the sphere the mirror was cut from. For a concave mirror it lies in front of the mirror; for a convex mirror, behind it.
- Radius of curvature ()** — the distance , the radius of that sphere.
- Principal axis — the straight line through and , meeting the mirror at right angles.
- **Principal focus () — the point on the principal axis where rays parallel to the axis meet after reflection (concave), or from which they appear** to diverge (convex). The distance is the **focal length ().
The relation between them:**
The focus sits exactly halfway between the pole and the centre of curvature.
Worked example. A concave mirror is cut from a sphere of radius . Then
so is in front of the pole and is in front of it.
And in reverse: a mirror of focal length has
Why concave mirrors are called converging. Parallel rays actually cross at , so the light really does arrive there and a real image can be caught on a screen. A convex mirror spreads the rays, so they never cross and is only a point they seem to come from — making every convex image virtual.
How do you draw a ray diagram for a concave mirror?
Draw two rays from the top of the object and see where they meet. Four standard rays are available, and any two will do.
- A ray parallel to the principal axis reflects **through .
- A ray through reflects parallel to the principal axis.
- A ray through strikes the mirror along its own normal and returns along the same path.
- A ray hitting the pole** reflects with about the principal axis.
Take the mirror above, with and at . The image changes character as the object moves in.
- Object far away (at infinity) — image **at , real, inverted, point-sized.
- Object beyond **, say at — image **between and , real, inverted, diminished.
- Object at **, exactly — image **at , real, inverted, same size.
- Object between and **, say at — image **beyond , real, inverted, magnified.
- Object at **, exactly — reflected rays come out parallel, so they never meet: no image is formed, or equivalently the image is at infinity.
- **Object between and **, say at — image behind the mirror, virtual, erect and magnified.
The pattern worth noticing. Every position outside gives a real, inverted image; only the position **inside ** gives a virtual erect one. And as the object approaches from outside, the image races away and grows.
Back to the spoon. Holding it at arm's length puts your face **beyond ** for such a sharply curved mirror, which is why the image is inverted and small. Bring the hollow side very close to your eye — inside — and the image flips to erect and magnified. Same spoon, both answers.
- A ray parallel to the principal axis reflects **through .
- A ray through reflects parallel to the principal axis.
- A ray through strikes the mirror along its own normal and returns along the same path.
- A ray hitting the pole** reflects with about the principal axis.
Take the mirror above, with and at . The image changes character as the object moves in.
- Object far away (at infinity) — image **at , real, inverted, point-sized.
- Object beyond **, say at — image **between and , real, inverted, diminished.
- Object at **, exactly — image **at , real, inverted, same size.
- Object between and **, say at — image **beyond , real, inverted, magnified.
- Object at **, exactly — reflected rays come out parallel, so they never meet: no image is formed, or equivalently the image is at infinity.
- **Object between and **, say at — image behind the mirror, virtual, erect and magnified.
The pattern worth noticing. Every position outside gives a real, inverted image; only the position **inside ** gives a virtual erect one. And as the object approaches from outside, the image races away and grows.
Back to the spoon. Holding it at arm's length puts your face **beyond ** for such a sharply curved mirror, which is why the image is inverted and small. Bring the hollow side very close to your eye — inside — and the image flips to erect and magnified. Same spoon, both answers.
Why does a convex mirror never give anything but a small erect image?
Because it diverges every beam, so the reflected rays never cross in front of it. They can only be traced backwards to an apparent meeting point behind the mirror.
For a convex mirror, whatever the object position, the image is:
- virtual — behind the mirror, never catchable on a screen
- erect — the right way up
- diminished — always smaller than the object
- **located between and ** — however far the object is
That last point is the interesting one. Move the object from a metre away to ten metres away and the image does not travel far behind the mirror; it creeps towards and stops. All of outside space is compressed into the tiny stretch between and .
Which is precisely what makes it useful. Because everything fits into that small region, a convex mirror shows a very wide field of view in a small area of glass. A driver glancing at a convex rear-view mirror sees several lanes at once, where a plane mirror of the same size would show only one.
The cost of that wide view. Objects look smaller than they are, so they also look farther away than they are. A vehicle that appears distant in a convex mirror may be closer than it seems — a boundary case with real consequences, and a fair exam question.
Contrast with the concave mirror of the previous section, where the image nature changed six times as the object moved. The convex mirror has exactly one answer for every position, which makes it the easier of the two to describe and the harder one to use for precise judgement.
For a convex mirror, whatever the object position, the image is:
- virtual — behind the mirror, never catchable on a screen
- erect — the right way up
- diminished — always smaller than the object
- **located between and ** — however far the object is
That last point is the interesting one. Move the object from a metre away to ten metres away and the image does not travel far behind the mirror; it creeps towards and stops. All of outside space is compressed into the tiny stretch between and .
Which is precisely what makes it useful. Because everything fits into that small region, a convex mirror shows a very wide field of view in a small area of glass. A driver glancing at a convex rear-view mirror sees several lanes at once, where a plane mirror of the same size would show only one.
The cost of that wide view. Objects look smaller than they are, so they also look farther away than they are. A vehicle that appears distant in a convex mirror may be closer than it seems — a boundary case with real consequences, and a fair exam question.
Contrast with the concave mirror of the previous section, where the image nature changed six times as the object moved. The convex mirror has exactly one answer for every position, which makes it the easier of the two to describe and the harder one to use for precise judgement.
Where are concave and convex mirrors actually used?
Each is chosen for exactly the property the previous sections established.
Concave mirrors — used when light must be concentrated or magnified.
- Vehicle headlights and torches. The bulb is placed at the focus, so rays leaving reflect parallel to the axis and form a strong straight beam that travels far. This is the parallel-ray rule used in reverse.
- Shaving and make-up mirrors. The face is held **inside , giving a virtual, erect, magnified image.
- A dentist's mirror, for the same magnifying reason.
- Solar cookers and solar concentrators**, gathering parallel sunlight to a hot point at .
- Reflectors behind a stage lamp, for the same reason as a headlight.
Convex mirrors — used when a wide view matters more than size.
- Vehicle rear-view and wing mirrors, for the wide field of view.
- Mirrors at blind corners in narrow lanes and in parking areas.
- Mirrors inside shops and buses, letting one person watch a large area.
- Street-light reflectors, spreading light over a broad stretch of road.
The design rule in one line. Concave to collect light or magnify a nearby object; convex to spread light or see more.
And note the deliberate choice of position in the headlight: the bulb is not placed anywhere convenient but exactly at , because only that position produces a parallel beam. Shift it slightly and the beam spreads or converges, which is why a loose headlight bulb dazzles oncoming traffic.
Concave mirrors — used when light must be concentrated or magnified.
- Vehicle headlights and torches. The bulb is placed at the focus, so rays leaving reflect parallel to the axis and form a strong straight beam that travels far. This is the parallel-ray rule used in reverse.
- Shaving and make-up mirrors. The face is held **inside , giving a virtual, erect, magnified image.
- A dentist's mirror, for the same magnifying reason.
- Solar cookers and solar concentrators**, gathering parallel sunlight to a hot point at .
- Reflectors behind a stage lamp, for the same reason as a headlight.
Convex mirrors — used when a wide view matters more than size.
- Vehicle rear-view and wing mirrors, for the wide field of view.
- Mirrors at blind corners in narrow lanes and in parking areas.
- Mirrors inside shops and buses, letting one person watch a large area.
- Street-light reflectors, spreading light over a broad stretch of road.
The design rule in one line. Concave to collect light or magnify a nearby object; convex to spread light or see more.
And note the deliberate choice of position in the headlight: the bulb is not placed anywhere convenient but exactly at , because only that position produces a parallel beam. Shift it slightly and the beam spreads or converges, which is why a loose headlight bulb dazzles oncoming traffic.
Exam tip
Exam tip: name the object position before describing the image
For a concave mirror, first state where the object is relative to and — beyond , at , between and , at , or inside . The image description follows automatically once the position is named.
Describe every image with three words: its nature (real or virtual), its attitude (inverted or erect), and its size (diminished, same or magnified). A question asking for the image expects all three.
Use in both directions. gives ; gives .
In a ray diagram, draw rays from the top of the object, use two of the standard rays, and mark the arrowheads. For a virtual image, extend the reflected rays backwards as dashed lines.
Remember real images are inverted and virtual images are erect — for mirrors there is no exception, so this pairing is a free self-check.
For a convex mirror, one answer covers every case: **virtual, erect, diminished, between and .
And for the headlight, say the bulb is at the focus** — not merely inside the mirror.
Describe every image with three words: its nature (real or virtual), its attitude (inverted or erect), and its size (diminished, same or magnified). A question asking for the image expects all three.
Use in both directions. gives ; gives .
In a ray diagram, draw rays from the top of the object, use two of the standard rays, and mark the arrowheads. For a virtual image, extend the reflected rays backwards as dashed lines.
Remember real images are inverted and virtual images are erect — for mirrors there is no exception, so this pairing is a free self-check.
For a convex mirror, one answer covers every case: **virtual, erect, diminished, between and .
And for the headlight, say the bulb is at the focus** — not merely inside the mirror.
Did you know
Why does a convex mirror fit a whole street into a small disc?
A plane mirror reflects a patch of the world the same size as itself. To see more, you need a bigger mirror.
A convex mirror escapes that limit by squeezing. Because it places every image — near or far — into the narrow region between the pole and the focus, the entire scene in front of it is compressed into a small area of glass. A disc the size of your palm can hold an image of a whole road junction.
Nothing is lost, but everything is shrunk, and detail goes with it. You can tell that a vehicle is approaching from the left, but not easily how far away it is.
That is the trade the shape forces on you: a wider view or a truer sense of size, never both from one mirror. It is also why vehicles carry a convex wing mirror for watching traffic and a plane or nearly plane interior mirror for judging distance.
A convex mirror escapes that limit by squeezing. Because it places every image — near or far — into the narrow region between the pole and the focus, the entire scene in front of it is compressed into a small area of glass. A disc the size of your palm can hold an image of a whole road junction.
Nothing is lost, but everything is shrunk, and detail goes with it. You can tell that a vehicle is approaching from the left, but not easily how far away it is.
That is the trade the shape forces on you: a wider view or a truer sense of size, never both from one mirror. It is also why vehicles carry a convex wing mirror for watching traffic and a plane or nearly plane interior mirror for judging distance.
Key takeaways
Spherical mirrors and ray diagrams: quick revision
- A spherical mirror is part of a sphere: **pole at its centre, centre of curvature , radius , principal axis** through and , and **principal focus ** at distance .
- , so gives , and gives .
- Concave mirrors converge (real focus, in front); convex mirrors diverge (virtual focus, behind).
- Ray rules: parallel to the axis reflects through ; through reflects parallel; through retraces its path; at the pole, .
- Concave images — at infinity: at , real, inverted, point. Beyond : between and , real, inverted, diminished. At : at , real, inverted, same size. Between and : beyond , real, inverted, magnified. At : no image (rays parallel). Inside : behind the mirror, virtual, erect, magnified.
- Convex images — always virtual, erect, diminished and **between and , whatever the object distance.
- Real images are inverted; virtual images are erect — always, for mirrors.
- Uses: concave for headlights (bulb at for a parallel beam), shaving mirrors, dentist's mirrors and solar cookers; convex for rear-view mirrors, blind corners and shop mirrors.
- Convex gives a wide field of view** but makes objects look smaller and farther than they are.
Sketch the six concave cases from memory now, then check them — being able to place the image without redrawing is what makes these questions quick.
- , so gives , and gives .
- Concave mirrors converge (real focus, in front); convex mirrors diverge (virtual focus, behind).
- Ray rules: parallel to the axis reflects through ; through reflects parallel; through retraces its path; at the pole, .
- Concave images — at infinity: at , real, inverted, point. Beyond : between and , real, inverted, diminished. At : at , real, inverted, same size. Between and : beyond , real, inverted, magnified. At : no image (rays parallel). Inside : behind the mirror, virtual, erect, magnified.
- Convex images — always virtual, erect, diminished and **between and , whatever the object distance.
- Real images are inverted; virtual images are erect — always, for mirrors.
- Uses: concave for headlights (bulb at for a parallel beam), shaving mirrors, dentist's mirrors and solar cookers; convex for rear-view mirrors, blind corners and shop mirrors.
- Convex gives a wide field of view** but makes objects look smaller and farther than they are.
Sketch the six concave cases from memory now, then check them — being able to place the image without redrawing is what makes these questions quick.