Light: Mirrors and Lenses

Sit in a room at night and switch off every light. Cover the windows so that not even street light comes in. Your eyes are wide open and perfectly healthy, and yet you see nothing at all. Bring in one small candle and the whole room comes back. This simple test tells you something important: your eyes do not send anything out to feel objects, they only receive light. We see an object only when light coming from that object enters our eyes.

Objects that make their own light are called luminous objects. The Sun, a burning candle, a glowing bulb and the red-hot coil of a heater are luminous. Most of the things around you are not. A notebook, a wall, the Moon and your own face give out no light of their own. They are illuminated objects: light from a luminous source falls on them, bounces off, and some of it reaches your eye. That bouncing back of light from a surface is called reflection, and it is the single idea behind every mirror you have ever used.

Light also travels in straight lines, and you can check this without any apparatus. Take three cardboard sheets, punch a small hole at the same height in each, stand them in a row and look through the holes at a candle placed beyond them. You can see the flame only while the three holes are in one straight line. Push the middle card slightly to one side and the flame vanishes at once, even though nothing solid has come in the way. The same straight-line travel is the reason a solid object casts a sharp shadow, and the reason you cannot see around a corner.

Because light moves in straight lines, we draw its path as a straight arrow called a ray. A ray is a drawing tool rather than a real thin thread of light, and a bundle of rays travelling together is called a beam. Ray diagrams are the language of this whole chapter. Once you can work out where a ray goes after it strikes a mirror or enters water, you can predict what kind of image will be formed, how big it will look and where a person has to stand to see it. Everything that follows, from the mirror on a scooter to the lens in your eye, is built on these two starting facts: light travels straight, and light bounces off surfaces.

Stand a plane mirror upright on a table and let a narrow strip of sunlight or a torch beam fall on it at a slant. The light neither passes through nor stops. It leaves the mirror at a slant on the other side. To describe this neatly, each part of the picture is given a name.

• The ray arriving at the mirror is the incident ray.
• The exact spot where it lands is the point of incidence.
• A line drawn perpendicular to the mirror at that spot is the normal. It is an imaginary reference line and not a real ray of light, so it is usually drawn dotted.
• The ray that leaves the mirror is the reflected ray.
• The angle between the incident ray and the normal is the angle of incidence. The angle between the reflected ray and the normal is the angle of reflection.

Notice carefully that both angles are measured from the normal and never from the surface of the mirror. Repeat that to yourself, because a slip here changes every answer that follows. If a ray comes in at 30 degrees to the mirror surface, its angle of incidence is 60 degrees, not 30 degrees.

Careful measurement of the two angles, for ray after ray, gives two rules that never fail.

1. The angle of incidence is equal to the angle of reflection.
2. The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.

The second law is easier to feel than to state. It says the reflected ray does not swing off sideways: the incoming ray, the normal and the outgoing ray can all be drawn on one flat sheet of paper. Stand a mirror upright on a table and aim a torch beam at it along the table top. The reflected beam also runs along the table top. It never lifts towards the ceiling or dips towards the floor.

One special case is worth remembering. If a ray travels along the normal, that is, if it strikes the surface straight on, the angle of incidence is zero, so the angle of reflection is also zero and the light returns along the very path it came by. That is exactly what happens when you look squarely into a mirror and see your own eyes looking back.

Now ask why a mirror shows a clear image while a whitewashed wall does not, when both reflect light. The answer is the smoothness of the surface. On a polished mirror a parallel beam stays parallel after reflection, and this is called regular reflection. On paper, cloth, wood or a wall, the surface is full of tiny bumps and hollows. Each bump behaves like a very small mirror facing a slightly different direction, so the normals at neighbouring points also point in different directions and the reflected rays scatter everywhere. This is diffuse reflection, also called irregular reflection. Here is the part that is often misunderstood: both laws are still obeyed at every single point of that rough surface. Diffuse reflection is not a failure of the laws, it is simply the result of a rough surface. It is also a blessing, because it is what lets every student in the class see the same blackboard from a different seat.

Stand about a metre in front of a plane mirror at home and study the image carefully. Five statements can be made about it, and together they describe every plane mirror image you will ever meet.

1. It is erect, standing the same way up as you do.
2. It is the same size as you, neither bigger nor smaller.
3. It is as far behind the mirror as you are in front of it. Step back half a metre and the image also moves back half a metre, so the gap between you and your image grows by a whole metre.
4. It is laterally inverted, which means left and right are interchanged.
5. It is virtual. Light never actually reaches the place where the image seems to be, so the image cannot be caught on a screen. Hold a sheet of paper behind the mirror and nothing at all appears on it.

Lateral inversion deserves a closer look, because it is easy to describe wrongly. Raise your right hand in front of a mirror. The figure facing you raises the hand on your right-hand side, but for that figure it is the left hand. A mirror does not turn things upside down. It swaps the side facing the mirror with the side away from it, and for a person standing upright that shows up as a left-and-right swap.

Two familiar consequences follow. The first is the writing on the front of an ambulance. It is painted reversed so that a driver ahead, glancing into the rear-view mirror, reads it the right way round and moves aside quickly. The second is the odd behaviour of letters. Hold a printed page up to a mirror. Letters such as A, H, I, M, O, T, U, V, W, X and Y look unchanged, because each of them is symmetrical about a vertical line down the middle. Letters such as B, E, F, G, J, L, N, P, Q, R, S and Z are clearly reversed. Try it with the digits, and then with your own name written in capitals.

Mirrors also work in pairs. Stand two plane mirrors upright with their shiny surfaces turned towards each other at right angles, put a small object in the corner between them, and you will count three images instead of one. Each mirror forms one image on its own, and the third is formed by light that bounces off both mirrors, one after the other, before reaching your eye. As the angle between the two mirrors is made smaller, the number of images increases. A kaleidoscope uses exactly this. Strips of mirror are fixed inside a tube at an angle, and a few coloured beads at one end become a repeating pattern that changes every time the tube is turned. A periscope uses a different arrangement: two plane mirrors are fixed parallel to each other inside a tube, each tilted at 45 degrees, so that light coming in at the top is turned down the tube and then turned again into the eye. With one, a person can see over a wall, over a crowd, or out of a submarine.

Take a clean steel spoon and hold it at arm's length. Look into the hollow side, the side that holds the dal. Your face appears upside down and much smaller. Now bring the spoon in slowly until it is very close, almost touching your nose, and the image turns upright and larger. The curve of a spoon is sharp, so this change happens only in the last centimetre or two, which is why the spoon has to come right up to your face. Turn the spoon over and look into the bulged back: the image is upright and small, and it stays small however you move the spoon. In those few seconds you have used a concave mirror and a convex mirror.

A spherical mirror is a small piece cut out of a hollow sphere with one surface polished. If the polished surface is the inner, caved-in one, the mirror is concave. If the polished surface is the outer, bulging one, the mirror is convex.

The difference in behaviour comes from what each one does to a parallel beam of light such as sunlight. A concave mirror brings the reflected rays together at a point in front of it. That point is called the focus, and a concave mirror is therefore a converging mirror. Hold one in sunlight with a piece of paper at the focus and a small, very bright spot appears; given enough time the paper begins to char, which shows that light energy has been collected into a tiny area. Do this outdoors with an adult present, and never let that bright spot fall on skin or turn the mirror towards anyone's face. A convex mirror does the opposite. The reflected rays spread apart, and if you trace them backwards they seem to come from a point behind the mirror. A convex mirror is a diverging mirror.

What image does each one form? The concave mirror is the interesting one, because its answer depends on where the object is. When the object is very close to the mirror, the image is enlarged, erect and virtual. That is why a concave mirror is used as a shaving mirror or a make-up mirror, and why a dentist holds a small concave mirror near a tooth to see a big clear picture of it. When the object is far away, the image is real and inverted, usually smaller, and it can be received on a screen. Turning the idea around, a lamp placed at the focus of a concave mirror sends out a straight parallel beam, and that is how a torch, a vehicle headlight and a searchlight throw light far ahead. A dish-shaped solar cooker uses the converging action instead: its large concave mirror catches the Sun's parallel rays and brings them together on the cooking pot, so the light falling on a wide dish is delivered to one small area.

The convex mirror is far simpler. Whatever the object and wherever it stands, the image is virtual, erect and smaller than the object. Making everything look smaller sounds like a disadvantage, but a smaller image means more of the surroundings fit into the same mirror, so a convex mirror gives a wide field of view. That is precisely what a driver needs, which is why the side mirrors of cars, buses and two-wheelers are convex, and why large convex mirrors are fixed at blind corners of narrow lanes and near the ceilings of shops so that the whole floor can be watched from one place.

Put a straight pencil into a glass tumbler half filled with water and look at it from the side. The pencil seems to break at the water surface, and the part under water looks thicker and shifted to one side. Lift the pencil out and it is as straight as ever. Nothing bent the pencil. What bent was the light.

Light travels fastest in empty space and almost as fast in air. When it enters water, glass, kerosene or any other transparent material, it slows down. When it comes back out into air, it speeds up again. This change of speed at the boundary between two media makes the ray change direction, and that change of direction is called refraction.

There is a simple pattern to which way the ray bends, and it is easiest to hold in mind if you always draw the normal at the surface first.

• Going from air into water or glass, that is, from a rarer medium into a denser one, the ray bends towards the normal.
• Coming out of water or glass into air, from a denser medium into a rarer one, the ray bends away from the normal.
• A ray that strikes the surface straight on, travelling along the normal, does not bend at all. Its speed still changes, but its direction does not.

A neat classroom experiment uses a rectangular glass slab. Send a ray in at a slant on one face. It bends towards the normal as it enters, travels in a straight line inside the glass, and bends away from the normal as it leaves the opposite face. The ray that finally comes out is parallel to the ray that went in, only shifted sideways. The two bendings cancel each other in direction but not in position, which is why a thick glass window slightly displaces what you see through it without tilting it.

Once you accept that light bends, the everyday puzzles fall into place. A coin lying at the bottom of a bucket of water appears raised, because light from the coin bends away from the normal as it leaves the water, and the eye, which always assumes that light arrived in a straight line, traces the ray back to a point higher than the coin really is. For exactly the same reason a pond, a canal or a swimming pool looks shallower than it is, and that is a real danger for anyone who cannot swim. A fish seen from the bank is not quite where it appears to be, so someone aiming a spear at the apparent position will miss it. Printed words under a thick glass slab look raised, as if they had floated up towards the top surface of the glass, though the letters themselves are not made any bigger. And the effect that matters most for the rest of this chapter is this: refraction at curved glass surfaces is the whole reason a lens can do anything at all.

A lens is a piece of transparent material, usually glass or plastic, with at least one curved surface. Light refracts once when it enters the lens and once more when it leaves, and the two bendings together give a lens its power to gather or to spread light.

There are two basic shapes, and you can tell them apart just by feeling them.

• A convex lens is thicker in the middle and thinner at the edges. It bends parallel rays inward so that they meet at a point called the focus. It is a converging lens.
• A concave lens is thinner in the middle and thicker at the edges. It bends parallel rays outward, and if those rays are traced backwards they seem to come from a point on the same side as the incoming light. It is a diverging lens.

Because a convex lens gathers light, sunlight passed through one makes a small bright spot on paper that can become hot enough to scorch it. This is a striking demonstration, but do it only with an adult present and out in the open. Never point a lens at a person or an animal, and never look at the Sun through any lens, since the gathered light can damage the eye at once.

The images formed by a convex lens depend on how far the object is, in much the same way as with a concave mirror. Hold a convex lens close to printed words and the letters appear enlarged, erect and virtual. This is the ordinary magnifying glass, used to read small print, to look at the parts of an insect and to examine the veins of a leaf. Now take the same lens to a wall on a bright day and point it at a distant window. Move the lens slowly back and forth and a small, upside-down, coloured picture of the window appears on the wall. That image is real and inverted, because light truly arrives there and can be received on a screen. The same behaviour lets a convex lens work inside a camera, inside a projector and inside the human eye.

A concave lens is much simpler, just like the convex mirror. Anything seen through it appears smaller, erect and virtual, and the image can never be taken on a screen. Its main everyday use is in spectacles for people who cannot see distant objects clearly, and it is also used together with other lenses inside instruments such as telescopes and binoculars to sharpen the final picture.

A quick way to keep all four devices straight is this. The two converging devices, the concave mirror and the convex lens, can give either an enlarged virtual image or a real inverted image, depending on how far the object is. The two diverging devices, the convex mirror and the concave lens, only ever give a small, erect, virtual image, no matter where the object is placed.

The eye is a small, almost round ball roughly the size of a large marble, and it uses nearly everything in this chapter. Light first passes through the cornea, the clear front window. Behind it lies the iris, the coloured ring that gives eyes their brown or black shade. The dark opening at the centre of the iris is the pupil. The iris works like the adjustable opening of a camera: in bright light it makes the pupil small so that less light gets in, and in dim light it opens the pupil wide to let more in. Watch a friend walk from a dark room into sunlight and you can see the pupil shrink.

Next comes the eye lens, a flexible convex lens held in place by tiny ciliary muscles. These muscles squeeze and relax to change the thickness of the lens so that objects both near and far can be brought into sharp focus. This adjustment is called accommodation, and it is the reason you can look up from a book at a distant tree without any effort. The lens throws light on to the retina, a screen at the back of the eye covered with light-sensitive cells. Since the eye lens is convex and the object is well beyond it, the image formed on the retina is real and inverted. The optic nerve carries the signals from the retina to the brain, and the brain interprets them so that we see the world the right way up.

The light-sensitive cells of the retina are of two kinds. Cones respond to bright light and let us tell colours apart. Rods respond to dim light but give no sense of colour, which is why everything looks grey in moonlight. At the exact spot where the optic nerve leaves the eye there are no such cells at all, so an image falling there is not seen. That spot is called the blind spot. One more useful fact is that an image stays on the retina for a very short time, roughly one-sixteenth of a second, after the object itself is taken away. This persistence of vision is why a series of still pictures shown quickly one after another is seen as smooth movement in a film.

A comfortable eye can focus on faraway objects and on objects as close as about 25 centimetres. Holding a book much closer than that strains the eye. Two common defects change these limits, and both are corrected by wearing a lens in front of the eye.

• Myopia, or short-sightedness. Nearby things are clear but distant things look blurred, because the image of a distant object is formed a little in front of the retina instead of on it. A concave lens spreads the light slightly before it enters the eye, which pushes the image back on to the retina.
• Hypermetropia, or long-sightedness. Distant things are clear but nearby things look blurred, because the image of a near object tends to form behind the retina. A convex lens gathers the light a little earlier, which brings the image forward on to the retina.

A third problem, cataract, is not corrected by spectacles at all. Here the eye lens itself slowly turns cloudy and vision becomes hazy, as though everything is behind a fogged window. A doctor removes the clouded lens by an operation and puts a clear artificial lens in its place. Simple care goes a long way with eyes. Read in good light and never in the dark or in a moving vehicle, keep the reading distance around 25 centimetres, take regular breaks from screens, wash the eyes with clean water, do not rub them with dirty hands, never stare at the Sun, and eat food rich in vitamin A such as papaya, carrot, mango, green leafy vegetables, milk and eggs. A long shortage of vitamin A makes it hard to see in dim light. If print or the blackboard starts looking blurred, get the eyes tested by a doctor rather than waiting.