Class 8 Science Chapter 10: Light: Mirrors and Lenses

A Spoon With Two Faces

Rohit was laying out the steel plates for dinner when he caught sight of himself in the bowl of a spoon. His face was upside down. He turned the spoon over, looked at the back of it, and there he was the right way up - but tiny. One spoon, two quite different pictures of the same face.

Why a Spoon Can Act as a Mirror

Anything polished enough to throw light back acts as a mirror, and a steel spoon is certainly that. So the spoon being a mirror is not the surprise. The surprise is the two pictures, because the bathroom mirror at home never does anything of the sort.

What a Flat Mirror Always Gives

Set that down as the baseline. A flat mirror, properly called a plane mirror, hands back a face the same size as the real one and the right way up, and it does that whether you stand close to it or across the room. Nothing in the picture changes as you move.

Mirrors That Are Not Flat

Neither face of a spoon is flat. A mirror whose reflecting surface is curved is called a curved mirror, and the kind met most often is shaped like a piece taken out of a hollow ball. Those are the spherical mirrors.

Only Two Ways To Curve

A surface can cave in or it can bulge out, and that is the whole choice. The bowl of the spoon caves in; the back of it bulges out. Each gets its own name, and the names are worth getting right the first time.

Concave and Convex

A spherical mirror whose reflecting surface curves inwards is a concave mirror. One whose reflecting surface curves outwards is a convex mirror. The bowl of the spoon behaved as a concave mirror and the back of it as a convex one.

A Way To Hold the Names

Concave has a cave in it, and a cave goes into a hillside. Convex starts the way exit does, and the surface of a convex mirror pushes out towards whoever is looking. One word in, one word out.

Drawing One on Paper

In a diagram each mirror is an arc, and the two arcs for the two mirrors are drawn facing opposite ways. The side that does not reflect is shaded in. That shading is not decoration: it is the only thing in the drawing that tells a reader which face the light is bouncing off.

The Rim Is a Circle

Look straight at a spherical mirror rather than from the side and the outline of its surface is circular. That follows from where the shape comes from - any piece cut out of a ball has a round edge.

Not Actually Cut From a Ball

The piece-of-a-sphere picture is a help, but no factory slices up glass spheres. A flat disc of glass is ground away and polished until its surface has the curve wanted, which is slower than it sounds and far more accurate.

The Coating Decides the Mirror

Then one face is coated with a thin layer of a shiny metal, usually aluminium. Coat the outer curve and the light has to reflect off the inner curve, which gives a concave mirror. Coat the inner curve instead and the outer curve does the reflecting, giving a convex mirror. Same piece of glass, either mirror.

Telling Them Apart by Looking Sideways

Put the two mirrors face up on a table and crouch until your eye is level with the table top. From there the dip of one and the bulge of the other are obvious, and you need not look into either of them to decide which is which.

Telling Them Apart by the Image

The other way is to use them. Hold the hollow one close and your face comes back enlarged; carry it slowly away and at some point the face turns over. The bulging one gives a small upright face wherever you hold it. A plane mirror gives the same size, upright, always.

The Shape Is Doing the Work

Nothing about the spoon changed between those two looks. Same steel, same polish, same room, same light. The direction of the curve was the only difference, and it was enough to turn a face over.

What to Carry Forward

A spherical mirror is a mirror whose reflecting surface is shaped like part of a hollow sphere. Curving inwards makes it concave and curving outwards makes it convex. Diagrams shade the face that does not reflect. The mirrors are ground from flat glass and then coated on one face, and that face decides which mirror you end up with.

Scenario:

A teacher opens the science store room and finds two unlabelled boxes of mirrors, each holding a dozen round mirrors of the same size in the same frames. The labels have come off, and the mirrors have to be sorted before the next class. One pupil suggests weighing them, since a thicker mirror ought to be heavier. A second suggests holding each one up to the window to see which lets more light through. A third picks one up, brings it close to her face. And says it is the enlarging kind, so the whole box must be that kind. And then finds that the next mirror she tries from the same box does not enlarge at all, which leaves the class stuck.

Analysis:

The first two suggestions cannot work. Both boxes hold mirrors of the same size in the same frames, so weighing them compares nothing useful. And a coated mirror does not let light through either way, so the window test gives the same answer for both. The third pupil had the right instinct but used the test carelessly. A concave mirror does enlarge a face held close, but it turns the face over once it is carried further away, so a single glance at one distance can mislead. There are two dependable tests. Lay each mirror down with its reflecting face upwards and put your eye level with the table: a concave surface dips away and a convex one rises towards you. Or use the image properly, moving the mirror as you look - a convex mirror keeps the face small and erect at every distance, while a concave one changes.

Activity:

Find three curved shiny surfaces at home - a spoon, a steel glass, a ladle - and sort them into inward-curving and outward-curving by the side-view test.

Title:

Try it at home: make two mirrors out of one spoon

Safety:

Use a spoon rather than a glass mirror, and do not carry a mirror or a spoon outdoors to catch the sunlight.

What You Notice:

The bowl behaves as a concave mirror: it enlarges your face up close and turns it over once you move the spoon away. The back behaves as a convex mirror, keeping your face small and upright at every distance. Your two side-view drawings should show one surface dipping away from your eye and the other rising towards it.

The shiny layer on a mirror is often aluminium, and it need be no thicker than a few hundred atoms to turn glass into a mirror.

A spoon is a poor spherical mirror in one way: its bowl is not a true piece of a sphere, which is why the image in it stretches oddly as you tilt it.

You can decide whether a mirror is concave or convex without ever looking into it, simply by dropping your eye to the level of its surface and looking along it from the side.

A cave goes in, an exit goes out — Concave has a cave in it, and a cave goes into a hillside, so a concave mirror curves inwards. Convex begins the way exit does, and its surface pushes out towards you.

Spoon front, spoon back — The bowl of a spoon is your concave mirror and the back of it is your convex mirror. Any time the two names slip, pick up a spoon and look.

A Row of Mirrors at the Science Centre

Meena had wandered away from her parents when she found a row of curved mirrors along one wall. In the first her own face came back enormous. Her brother, standing a little further back, was upside down in it. A few steps along she met a tiny, neat version of herself. Three pictures of two people, all from mirrors.

Why That Was Worth Asking About

She had used a mirror all her life without anything of the sort happening. The mirror at home gives her face back at its own size and the right way up, and it does that whether she is combing her hair or standing by the door. So the wall of mirrors was doing something a flat mirror never does.

The Experiment That Settles It

The honest way to sort this out is to stand a concave and a convex mirror side by side, put a small toy in front of them three or four centimetres away, and look. Then slide the toy slowly back and keep looking. Write down two things each time: how big the picture is, and whether it is the right way up.

The Concave Mirror With the Object Close

Up close the concave mirror gives an erect picture, the right way up, and larger than the toy itself. That part feels friendly, because a bigger picture of a small thing is a useful thing for a mirror to do.

Then Move the Object Back

Carry on sliding the toy away and the picture turns over. From that point on the concave mirror gives an inverted picture. It is large to begin with, and then it shrinks steadily the further the toy goes.

So a Concave Mirror Has No One Answer

That is the thing to hold on to. Ask what a concave mirror does to an image and the only honest reply is another question: how far away is the object? The picture can be enlarged, the same size or diminished, and erect or inverted, and the distance decides.

The Convex Mirror Is Far More Predictable

Now the convex mirror, over the same range of distances. It gives an erect picture every time, and a diminished one every time. Slide the toy away and the picture does shrink a little more, but it never turns over and it is never bigger than the toy.

The Plane Mirror as the Baseline

Keep the flat mirror beside them for comparison. It gives an erect picture of exactly the same size at every distance, which is what made Meena’s row of mirrors surprising in the first place.

One Thing All Three Share

Lateral inversion. Hold up your right hand to a plane mirror and the hand that comes back is on the left. That left-for-right swap happens in a concave mirror and a convex mirror too, so it is no help at all in telling the three apart.

Naming a Mirror From Its Image

Which makes a tidy test. Same size and erect at every distance, and it is plane. Always erect and always smaller, and it is convex. Changes with distance and turns over, and it is concave. No need to touch the glass.

Where a Concave Mirror Earns Its Keep

Look inside a torch, or the headlight of a car or a scooter, and the shiny cup behind the bulb is concave. A dentist uses one too, a small concave mirror on a handle, because held close to a tooth it gives an enlarged view of it.

The Largest Mirrors We Make

Most modern telescopes are reflecting telescopes, and the main mirror in one is a large concave mirror. Some of them are measured in metres across, which makes them among the most carefully ground pieces of glass anywhere.

Why Vehicles Carry Convex Mirrors

The side-view mirror on a scooter or a car is convex. It gives an erect picture of the traffic behind, smaller than the real vehicles, and because the surface bulges outwards it gathers in a much wider stretch of road than a flat mirror of the same size could.

Convex Mirrors on the Road and in Shops

At a blind bend or a crossing, a convex mirror on a pole lets drivers coming from either side see the other road, which prevents collisions. Big shops fit them high in a corner for the same reason, to watch a large area at once and deter theft.

What to Carry Forward

A concave mirror gives an image that depends on distance: erect and enlarged close up, inverted and shrinking further away. A convex mirror always gives an erect, diminished image. A plane mirror always gives an erect image as large as the object. Lateral inversion happens in all three. Concave mirrors go into torches, headlights, dental mirrors and telescopes; convex mirrors into side-view, road safety and surveillance mirrors.

Scenario:

A shopkeeper wants one mirror that will let him watch the whole floor of his shop from the counter. He is shown three of the same size and the same price. He holds each one up at arm’s length and looks at his own face in it. In the first his face is its ordinary size. In the second it is large and slightly blurred at the edges, which impresses him, and he decides a mirror that shows more of his face must show more of the shop. In the third his face is small, which he takes as a fault in the glass. He buys the second, fixes it high in the corner, and finds he can see one aisle and part of the counter, and nothing else at all.

Analysis:

He tested the mirrors on the wrong thing. Holding a face at arm’s length is the close-up case. And in that case a concave mirror enlarges - which is what impressed him about the second mirror and told him it was concave. But enlarging a nearby face is the opposite of what he needs. A mirror that spreads one aisle across the whole of its surface has no room left for the rest of the shop. And once he looks at the far end of the floor the concave mirror will invert it as well. The third mirror, the one he rejected, was the convex one. It made his face small for exactly the reason he wanted. An outward curve gathers a wide area into a small image, so a single mirror in the corner can hold the whole floor at once, erect and easy to read. The first was a plane mirror and would have shown no more than a window of the same size.

Activity:

Look for curved mirrors on your way to school - at bends, in shops, on vehicles - and write beside each whether it bulges out or dips in, and what job it is doing.

Title:

Try it at home: test three mirrors with one toy

Safety:

Handle the mirrors over a table rather than over a hard floor, and do not carry them outside to catch the sunlight.

What You Notice:

Your table should show the plane mirror unchanged at all three distances and the convex mirror erect and smaller at all three. The concave mirror should start erect and enlarged and then turn over, shrinking as the toy goes further. The raised right hand comes back as a left hand in every one of the three, which is why that test identifies nothing.

The warning on a vehicle side-view mirror exists because the mirror is convex. A diminished image reads as a distant one, so vehicles behind look further away than they really are.

The main mirror of a large reflecting telescope is a concave mirror several metres across, and its surface is ground accurate to a small fraction of the width of a human hair.

A shop fits its surveillance mirror high in a corner rather than at eye level, because a convex mirror placed there takes in almost the whole floor at once.

Convex is constant, concave is conditional — A convex mirror answers the same way every time: erect and smaller. A concave mirror answers "it depends", and what it depends on is how far away the object is.

Close and clear, far and flipped — For a concave mirror: with the object close the image is erect and enlarged; once the object is far the image is flipped over and shrinking.

A Comb, a Torch and One Slit

Cover every gap of a comb with black paper except one in the middle, stand the comb upright with a paper clip, and shine a torch through it. What comes out is a single thin beam running flat along a sheet of white paper. Stand a plane mirror upright on the paper and let the beam fall on it.

Move the Torch and the Beam Answers

Shift the comb a little so the beam strikes the mirror at a different angle. The beam that comes back swings round to a new direction. Do it several times and the reflected beam moves every time, which means the two directions are tied together by some rule. The rest of the topic is that rule.

Drawing Light as a Ray

To write the rule down we need to draw light, and light is drawn as a straight line with an arrow on it. Such a line is called a ray, and the arrow shows which way the light is travelling. Straight lines are honest here, because light does travel in a straight line.

Two Rays With Names

Draw a line for the mirror, then the beam arriving and the beam leaving. The ray that falls on the mirror is the incident ray. The ray that returns off the mirror is the reflected ray. Two rays, two names, and the whole of what follows is about the angle between them.

The Point of Incidence

The incident ray meets the mirror at one place, and that place is called the point of incidence. It is usually labelled O. Everything else in the drawing is measured at that point, so it is worth marking clearly.

A Line That Is Not There

Now take the mirror away and draw, from the point of incidence, a line at exactly ninety degrees to the line of the mirror. That line is the normal to the mirror, drawn where the arriving ray strikes it. No light travels along it and nothing in the apparatus corresponds to it. It is drawn so that angles can be measured from it.

Two Angles, Measured From the Normal

The angle the incident ray makes with the normal is the angle of incidence, written i. The angle the reflected ray makes with the normal is the angle of reflection, written r. Both are measured from the normal, never from the mirror, and forgetting that is where most mistakes in this topic come from.

The First Law of Reflection

Measure i and r with a protractor, write them in a table, change the angle and do it again. The two columns come out nearly equal every time, and nearly is only the apparatus being imperfect. The angle of incidence equals the angle of reflection. That is the first law of reflection.

Doing the Measuring Honestly

A single pair of readings proves very little, which is why the activity asks for several. If one pair disagrees, suspect a thick beam, a tilted mirror or a badly drawn normal before you suspect the law.

Straight Down the Normal

There is one case worth trying on purpose: aim the beam along the normal itself. Now the incident ray lies on the normal, so the angle of incidence is zero. The light comes straight back the way it came, so the angle of reflection is zero too. The law still holds, with both angles at nothing at all.

Angles From the Mirror Are Not the Answer

A question may give the angle a ray makes with the mirror rather than with the normal, and the two add up to ninety degrees. A ray at forty degrees to the normal reflects at forty degrees to the normal, which is fifty degrees from the mirror. Read carefully which line the angle is measured from.

The Second Law, and a Sheet of Paper

The second law needs a different experiment. Put the mirror on a stiff sheet of chart paper with part of the sheet hanging over the edge of the table. The reflected beam shows up on that overhanging part. Now fold the overhanging part down along the edge of the table.

Why the Beam Disappears

The reflected beam vanishes from the folded part, and comes back as soon as the paper is flattened again. Folding the paper moved that piece of it out of the flat surface the beam was travelling in. So the incident ray, the reflected ray and the normal drawn where they meet the mirror all lie in one plane. That is the second law of reflection.

The Laws Hold for Curved Mirrors Too

Both laws are laws about reflection, not about flat mirrors, and they hold for plane, concave and convex mirrors alike. Each separate ray striking a curved mirror obeys them exactly. What makes a curved mirror behave differently is that the surface tilts from point to point, so neighbouring rays get different normals.

What to Carry Forward

Light is drawn as a ray. The ray arriving is the incident ray and the ray leaving is the reflected ray; they meet the mirror where the arriving ray strikes. The normal is at ninety degrees to the surface there, and both angles are measured from it. The angle of incidence equals the angle of reflection, and the incident ray, the reflected ray and the normal lie in one plane. Both laws apply to every mirror.

Scenario:

Four pupils set up the comb, the torch and a plane mirror and measure the two angles six times. Five of their pairs agree within a degree or two, but the sixth reads nineteen degrees of incidence against seventy-one of reflection. One of them announces that the first law has been disproved. A second says the torch must have moved. A third notices that the figures add up to ninety and suggests they simply write down the average of the two, which would be forty-five, and move on. The fourth wants to repeat the reading but cannot say what to change.

Analysis:

The third pupil is closest to the answer without seeing it. Nineteen and seventy-one adding to ninety is not a coincidence. It is the signature of one angle having been measured from the normal and the other from the mirror. The reflected ray really is nineteen degrees from the normal, which is the law holding exactly, and seventy-one is that same ray measured from the mirror surface instead. So nothing has been disproved and the torch has not moved. Averaging the two would be the worst move of all, because it throws away a correct reading and a correct one measured the wrong way and produces a number that means nothing. What to change is clear enough once the cause is seen: draw the normal first, dotted, and measure both angles from it.

Activity:

Take any reflection drawing in your notebook and write beside each marked angle which line it is measured from. Any angle you cannot label that way is one to redraw.

Title:

Try it at home: measure both angles five times

Safety:

Do not shine the torch into anybody’s eyes, and never use sunlight in place of the torch for this.

What You Notice:

Your five pairs should agree within a degree or two, which is the first law of reflection. Where a pair disagrees by more than that, check whether the beam was thick, whether the mirror was leaning. Or whether your dotted line was really at ninety degrees. And check that you measured both angles from the dotted line rather than one of them from the mirror.

The normal is the only line in a ray diagram that no light travels along. It is drawn purely so that angles have a reference, and it is usually shown dotted for that reason.

Aim a beam straight along the normal and it comes back along its own path. Both angles are zero, which is the one case where the incident and reflected rays sit on top of each other.

If a careful pair of readings disagree, the apparatus is almost always the culprit: a wide beam, a mirror leaning back, or a normal drawn a few degrees off ninety.

Both angles live on the normal — Neither angle is measured from the mirror. Find the normal first, at ninety degrees to the surface, and measure both the incident and the reflected ray from that line.

i equals r, and all three in one plane — Two laws, said in one breath. The first is about the sizes of the angles; the second is about the flat surface that the two rays and the normal share.

This Time, Uncover the Whole Comb

For the laws of reflection one slit was enough. Now leave many of the comb’s gaps open instead of one, and the torch sends out a whole set of thin beams running side by side along the paper. They start out parallel, and that is the point of the arrangement: send a parallel set at a mirror and watch what comes back.

The Plane Mirror Answers Plainly

Let the set fall on a plane mirror first. The beams that come back are still parallel to one another. They have changed direction together, as a group, but the spacing between them has not changed at all.

The Concave Mirror Brings Them Together

Swap in a concave mirror. The reflected beams lean towards each other and close up as they travel, meeting near a point in front of the mirror. A set of beams that draws together like that is said to converge.

The Convex Mirror Pushes Them Apart

Now the convex mirror. The reflected beams lean away from each other and the gaps between them widen as they travel. A set of beams that spreads like that is said to diverge.

Two Words Worth Keeping

So a concave mirror converges a parallel beam and a convex mirror diverges it. Those two words will come back in the next topic for lenses, where exactly the same pair of behaviours appears.

No Law Has Been Broken Here

It is tempting to think the curved mirror is doing something the laws of reflection do not cover. It is not. Take any single beam in the set: it has its own point of incidence, its own normal, and it leaves at an angle equal to the angle it arrived at.

Why the Curve Does It

What the curve changes is the normal. On a flat mirror every point has the same normal direction, so parallel rays all turn through the same angle and stay parallel. On a curved mirror the surface tilts from point to point, so each beam meets a differently tilted piece of surface and gets a different normal. The beams turn through different angles, and either close up or spread.

A Mirror That Gathers Sunlight

If a concave mirror draws a parallel set of beams to a point, then it should be able to do that with sunlight, because the Sun is so far away that the light reaching us arrives in a very nearly parallel set. That is a prediction worth testing with care.

Aiming It at the Sun

Hold a concave mirror so that its reflecting face is towards the Sun, and catch the light it throws back on a sheet of thin paper. Move the paper nearer and further until the patch of light on it is as small and as bright as you can make it.

Safety First, and Why

This one activity needs an adult with you, and two rules. Never look at the Sun, and never look into a mirror that is facing the Sun; that much light reaching the eye can damage it. And point the reflected light at the paper only, never towards anyone’s face.

What the Bright Spot Is

The small bright patch is a great deal of sunlight that fell on the whole face of the mirror, brought together into a tiny area. The mirror has not added anything to the light. It has only collected what was spread over a wide face and concentrated it.

Hot Enough to Burn

Hold the mirror and the paper steady for a few minutes and the paper begins to darken, then smoke, and can catch fire. Light carries energy, and concentrating that much of it into a small spot produces enough heat at that spot to set paper alight.

Mirrors Built for That Job

A device that uses mirrors, or lenses, to gather sunlight into a small area is called a solar concentrator. It is the same idea as the mirror and the thin paper, built at a useful size and aimed properly.

Steam, Cooking and Melting Steel

What the concentrated sunlight is used for is heat. It can boil a liquid to raise steam, and steam can be made to generate electricity. Large solar cookers work this way, and so does a solar furnace, where the temperature at the spot is high enough to melt steel.

What to Carry Forward

A parallel set of beams stays parallel off a plane mirror, converges off a concave mirror and diverges off a convex mirror. Every individual ray still obeys both laws of reflection; it is the tilting of the curved surface, and so of the normals, that separates the three cases. A concave mirror aimed at the Sun concentrates sunlight into a hot bright spot, which is the principle of solar concentrators, solar cookers and solar furnaces.

Scenario:

A school in a village is given a solar cooker: a wide dish lined with mirror panels and a stand to hold a black pot where the panels point. On the first afternoon the water in the pot barely warms. The caretaker checks the mirrors, which are clean, and the sky, which is clear. One teacher suggests the dish must be too small and a bigger one should be asked for. A pupil notices that the pot has been hung much lower than the bracket allows, to keep it steady in the wind. And that the patch of light on the bottom of the pot is wide and pale rather than small and fierce. Another pupil says the dish should be turned to face the Sun squarely, since it is tilted well away from it.

Analysis:

The two pupils between them have the answer. And the teacher’s suggestion would waste money. The dish of mirror panels is a concave reflecting surface, and it converges the nearly parallel sunlight falling on it towards a point. The heat depends on getting all of that light into the smallest area, which is why a wide pale patch means a cool pot and a small fierce patch means a hot one. Hanging the pot lower than the bracket puts it away from where the light comes together, so the patch spreads out. Turning the dish away from the Sun is the second fault. Light arriving at an angle across the dish is both less light and not properly converged. Raise the pot back to the bracket and aim the dish squarely at the Sun, and the same dish will boil the water.

Activity:

Find out whether any solar cooker or solar water heater is used near you, and write down whether its reflecting surface caves inwards or bulges outwards, and why.

Title:

Try it at home: converge a torch beam with a steel spoon

Safety:

Use the torch and not sunlight for this one, and do not shine the torch into anybody’s eyes.

What You Notice:

Your traces should show the beams from the plane mirror still evenly spaced, the beams from the concave mirror closing up towards a point. And the beams from the convex mirror spreading apart. If a spoon is used in place of the mirrors, the bowl gives the converging set and the back the diverging one.

Sunlight reaches us as a very nearly parallel set of rays, which is only because the Sun is so far away. That is what makes a concave mirror able to bring it to so small a spot.

The mirror adds no light at all. Every bit of brightness in the spot fell on the face of the mirror first and was simply gathered into a smaller area.

A solar furnace can reach a temperature high enough to melt steel, using nothing but sunlight and a careful arrangement of mirrors.

Caved in collects, bulging out broadcasts — The concave mirror caves in and collects a parallel beam to a point. The convex mirror bulges out and broadcasts the beam outwards in all directions.

Converge means come together — Converge shares its start with "come"; diverge shares its start with "divide". One brings the beams together, the other divides them.

A Window Tells You Nothing

Look out through a flat window pane at a tree and the tree looks the size and shape it would look with nothing in the way. Flat transparent glass leaves things alone. The mirrors in this chapter were interesting because they were curved, so the obvious question is what happens when a transparent thing is curved instead.

Making a Curved Piece of Water

Rub a very thin film of oil or wax over a flat strip of clear plastic or glass, then put one small drop of water on the greased patch. The film is there to stop the water spreading out: on it the drop pulls itself into a neat, round bead instead. Look at the bead sideways and its surface is curved outwards.

What the Drop Does to the Letters

Lay a printed page under the strip so that some words sit directly beneath the drop, and look down through the drop. The letters under it are bigger than the letters on either side. Nothing was done to the paper, so the curved piece of water has changed how the print looks.

That Drop Is a Lens

Which is exactly what a magnifying glass does for small print. The drop of water, with its curved outward surface, is behaving as a simple lens, and a magnifying glass is a lens made properly out of glass and given a handle.

What a Lens Is

A lens is a transparent piece of material, commonly glass or plastic, carrying curved surfaces. Transparent matters: a mirror is coated so that light cannot get through it, and a lens is not. And like mirrors, lenses come in two kinds.

The Convex Lens

A lens that is thicker at the middle than at its edges is a convex lens. Held between your fingers, it feels fat in the centre and thins away towards the rim. The water drop was a convex lens, and so is a magnifying glass.

The Concave Lens

A lens that is thicker at its edges than at the middle is a concave lens. It feels the other way round in the hand, thin in the centre and thickening towards the rim. In a diagram it is drawn with its two faces curving inwards.

Through a Lens, Not In It

Here is the real difference from a mirror. Light passes through a lens, so you look at a thing through a lens, whereas with a mirror you look at the image in it. Light never gets through a mirror at all, because of the coating.

Looking Through a Convex Lens, Object Close

Stand a convex lens upright in a holder, put a small object just behind it, and view the object through the lens, looking from its far side. It appears erect and larger than it really is. That is the magnifying-glass case.

Then Move the Object Back

Slide the object further from the lens and keep watching. At some point it appears inverted. It is large at first and then gets smaller as the object goes further away, which is the same pattern a concave mirror followed.

The Concave Lens Is Steadier

Now do the same with a concave lens. The object appears erect and smaller than it is, and it keeps doing that at every distance. Its size changes a little as the object moves away, but it never turns over.

Parallel Beams, and a Flat Plate First

Use the comb again to make several parallel beams, and stand a thin flat glass plate in their path. The beams go straight through and come out parallel, so flat transparent glass really does leave light alone. That is the control to compare the lenses against.

Converging Lens, Diverging Lens

Swap the plate for a convex lens and the beams close up on the far side: the convex lens converges them, which is why it is also called a converging lens. Swap in a concave lens and they spread apart, so a concave lens is also called a diverging lens.

Burning Paper, and Where Lenses Are Used

Since a convex lens converges light, it can be aimed at the Sun to make a hot bright spot on paper, just as a concave mirror can, and the same safety rules apply: never look at the Sun through a lens. Lenses are everywhere - in spectacles, in cameras, in telescopes and microscopes - and there is a convex lens inside each of your eyes, one that can change its own shape, which is how you can read a page and then look at something far off.

What to Carry Forward

A lens is transparent, with curved surfaces, and you look through it. A convex lens is thicker in the middle and converges light; close up it gives an erect enlarged view, and further away an inverted one that shrinks. A concave lens is thicker at the edges and diverges light, always giving an erect, diminished view. A flat glass plate does neither.

Scenario:

An optician’s apprentice is handed a case holding two pairs of spectacles whose labels have come off. One pair was ordered for a reader who cannot see small print clearly, the other for someone who cannot see distant signs. Both pairs look much alike at a glance. The apprentice holds the first pair over a printed page and the letters look bigger; over the second pair they look slightly smaller. He then runs a fingertip across each lens and finds the first fat in the centre and thinning to the rim. And the second pinched at the centre and thickening to the rim. A colleague tells him to label the fat one concave, since its surface is the one that dips.

Analysis:

The apprentice’s two tests agree with each other and his colleague is wrong. A lens thicker at the middle than at its edges is a convex lens, and the test with the printed page confirms it. Held over print, a convex lens gives an erect and enlarged view, which is the magnifying case. The second lens, pinched at the centre and thicker at the rim, is a concave lens. And what is seen through it is erect and diminished at every distance - which is exactly what he saw. The colleague has slipped on the naming, probably by carrying the mirror words across. A concave mirror has a surface that dips, but for a lens the name follows the thickness at the centre, and the two families converge and diverge the other way round. So the fat-centred pair is convex and belongs to the reader, and the pinched pair is concave.

Activity:

Look at any pair of spectacles at home and run a fingertip from the centre of a lens to its rim, then write down whether that lens is convex or concave.

Title:

Try it at home: make a lens out of a drop of water

Safety:

Use cooking oil rather than anything from a workshop, and do not carry the strip outdoors to look at the Sun through the drop.

What You Notice:

The surface of the drop curves outwards, which makes it a simple convex lens. And the words beneath it look larger and the right way up - the magnifying case. As you raise the strip the words grow for a while and then become hard to read. And with a large enough drop they turn over, which is the same thing a glass convex lens does when the object is moved away from it.

The thin film of oil or wax under the water drop is not part of the optics. It is there only to stop the water spreading out, so that the drop keeps a properly curved surface.

A convex lens and a concave mirror behave alike in converging light, while a concave lens and a convex mirror both spread it. The names run opposite ways for the two families.

The lens inside your eye changes shape as you shift your gaze from a page to a distant hill, which is something no lens made of glass can do.

Fat in the middle, converges — A convex lens is fat in the middle and brings light together. A concave lens is thin in the middle and spreads light out. Feel the middle of the lens and you know which it is.

In a mirror, through a lens — The image is seen in a mirror, because the coating stops the light. A thing is seen through a lens, because a lens is transparent.