Light: Mirrors and Lenses

Why This Matters

Have you ever looked at yourself in the back of a steel spoon? Your face looks huge and stretched. Flip the spoon over, look at the other side, and suddenly you are tiny and upside down. Same spoon. Same face. Two completely different pictures.

This is exactly what happened to a girl named Meena at a science centre. She walked up to a row of curved mirrors. In one, her face looked enormous. In the next, she was a tiny version of herself. Her brother, standing a little farther back, appeared upside down! She was puzzled, because she remembered that an ordinary mirror at home shows you just as you are.

So what is going on? Why do some mirrors flip you, some shrink you, and some blow you up like a balloon?

And it is not just mirrors. Look at a pencil standing in a glass of water — it looks broken at the surface. Look through a magnifying glass — tiny letters become big. Your own side-view mirror on a scooter even carries a warning: “Objects in mirror are closer than they appear.”

All of this is the science of light — how it bounces, how it bends, and how mirrors and lenses use those tricks. By the end of this chapter, none of it will be a mystery. You will know exactly why.

The Big Idea

Almost everything you see, you see because of reflected light. Light from a source (the Sun, a bulb) hits an object, bounces off it, and travels in straight lines into your eye. A mirror is just a very smooth, shiny surface that bounces light in a neat, organised way — so neat that it forms an image. When the mirror is flat, the image looks just like you. When the mirror is curved, it bends the bouncing rays together or apart, and the image changes size or flips over. A lens plays the same game but with light passing through it instead of bouncing off. Master two simple ideas — light reflects off surfaces and bends when it changes speed — and every mirror and lens in this chapter will make perfect sense.

Let’s Break It Down

First, how do we even see anything?

Before mirrors, let us settle one thing: why can you see this page at all?

A few things in the world make their own light — the Sun, a bulb, a flame, a firefly. But most things do not. A book, an apple, a wall, your friend’s face — none of them glow on their own. So how do you see them?

The answer is reflection. Light from a source falls on the object, and the object throws some of that light back. That thrown-back light enters your eye, and only then do you see the object. Turn off every light in a windowless room and you see nothing — not because the objects vanished, but because there is no light to bounce off them.

We lean on this idea all through the chapter, so let us lock it in with a quick refresher.

Figure 10.1 below shows this everyday bouncing of light from a light source, to an object, and into your eye.

Tap to zoom

Reflection and its two laws

So light bounces off surfaces. But it does not bounce just any old way — it follows two strict rules. These are the laws of reflection. Let us build them up with the right words first.

When a ray of light hits a mirror, the ray going in is called the incident ray. The ray coming back is called the reflected ray. Now here is the clever part. At the exact spot where the ray hits, we draw an imaginary line straight out from the mirror, at 90° to its surface. This line is called the normal. (“Normal” here just means a line at a right angle to the surface — nothing to do with “ordinary”.)

We measure both angles from this normal, not from the mirror:

• The angle between the incident ray and the normal is the angle of incidence, written i.
• The angle between the reflected ray and the normal is the angle of reflection, written r.

Now the first law. Let us see it as a picture before we say it in words.

Tap to zoom

As Figure 10.2 shows, when i = 40°, the reflected ray also leaves at r = 40°. Change the angle of the incoming ray and the reflected ray shifts to match — but i and r always stay equal. That is the first law:

Law 1: The angle of incidence is equal to the angle of reflection (i = r).

Here is a neat special case to fix the idea. If the ray comes straight down along the normal, then i = 0°. The light has no sideways lean at all, so it has no reason to bounce off to one side. It simply bounces straight back the way it came, with r = 0°. Both angles are zero.

Now the second law. It is about which flat sheet (plane) the rays live on. Imagine the incident ray, the normal and the reflected ray all drawn on a single flat sheet of paper. The second law says they really do all sit on that one sheet — none of them lifts off to the side.

Law 2: The incident ray, the normal, and the reflected ray all lie in the same plane.

How do we know this is true? Picture shining a beam onto a mirror placed on a flat sheet, with part of the sheet sticking out over the edge of the table. The reflected beam runs neatly along the flat sheet. Now fold that sticking-out part downwards. The reflected beam vanishes from it! That is because folding the paper made a new plane, and the reflected ray was never on that new plane — it stays on the original flat one, together with the incident ray and the normal.

Let us make sure the wording of the first law is crystal clear.

Why do the angles come out equal?

NCERT tells you i = r and moves on. But why should the bounce be so perfectly balanced? Let us see the reason, because it is beautiful and simple.

Think of throwing a rubber ball at a smooth floor. If you throw it straight down, it bounces straight back up. If you throw it at a slant, it bounces off at the same slant on the other side — a gentle throw makes a gentle bounce, a steep throw makes a steep bounce. Light behaves like this perfect, no-energy-lost bounce.

Here is the deeper reason. Light always takes the quickest path between two points. Imagine a lifeguard on a beach who must run along the sand and then swim out to a person in the sea. To save the most time, there is one best spot to enter the water. Work out that fastest path and it turns out the angle coming in (over the sand) matches the angle going out (the line to the swimmer), measured from the line straight out to sea — exactly like i = r measured from the normal. Light “chooses” the path that gets it from the source to your eye in the least time, and that path is the one where the two angles are equal. Nature is just being efficient. That is why the bounce is so perfectly symmetric, as you saw in Figure 10.2.

The image in a plane mirror

You look in a flat bathroom mirror every day. The image you see has four clear features. Let us list them, then explain the strangest one.

• It is upright (erect) — your head is up, not down.
• It is the same size as you.
• It appears to be behind the mirror, the same distance back as you are in front.
• It is laterally inverted — left and right are swapped.

The first three are easy to accept. But why does the image look like it is behind a solid mirror, where there is only a wall? Figure 10.3 below shows the trick your eye plays.

Tap to zoom

So the image is not really behind the mirror — no light goes there. Your eye just traces the reflected rays backwards in a straight line and lands behind the glass. An image like this, where no real light meets and which you cannot catch on a screen, is called a virtual image.

Now the famous left-right flip. Why does a mirror swap left and right but not up and down? Figure 10.4 below makes it clear.

Tap to zoom

Here is the honest explanation. The mirror does not really swap left for right. It swaps front and back — it flips the part of you facing the mirror to face away. Think of pressing a wet stamp onto paper: the side touching the paper gets flipped over. Because we are roughly the same on our left and right, our brain reads that front-back flip as a left-right swap. (Up and down are not affected, because the flip is along the line pointing into the mirror, not up the body.)

This is why the word AMBULANCE is painted reversed on the front of the vehicle. A driver ahead glances in their mirror, the mirror flips it back, and they read “AMBULANCE” correctly — and pull aside.

Curved mirrors: concave and convex

A flat mirror is only the start. A spherical mirror is a mirror whose surface is curved, like a small piece cut from a hollow ball. There are two kinds, and you already met them on a spoon.

• A concave mirror curves inwards — like the inside (the bowl) of a spoon.
• A convex mirror curves outwards — like the back of a spoon.

Why do these change the image? Because of the very same law of reflection (i = r), but now the surface is curved, so the normal points in a slightly different direction at every spot. The result is that parallel rays do not stay parallel after bouncing. Figure 10.5 below shows what happens.

Tap to zoom

This converging power of a concave mirror is genuinely useful — and a little dangerous. Hold a concave mirror facing the Sun and let it gather the sunlight onto a small spot of paper. So much light energy piles up at that point that the paper can heat up and even start to burn. Big versions of this idea, called solar concentrators, focus sunlight to heat water into steam and run machines, or even to melt steel in a solar furnace.

Now, what kind of image does each curved mirror give? This is what puzzled Meena. The key is how far the object is from the mirror.

For a concave mirror: when the object is close, the image is erect and enlarged (bigger than the object). As you move the object farther away, the image flips to inverted, and it keeps getting smaller. That is why Meena looked huge when close, but her brother, standing farther back, was upside down.

For a convex mirror: the image is always erect and diminished (smaller than the object), no matter where the object is. As the object moves away, the image just gets a little smaller. Because it shrinks everything, a convex mirror packs a wide view into a small mirror.

Figure 10.6 below puts all three mirrors side by side with the image each gives and where we use it.

Tap to zoom

This explains the warning “Objects in mirror are closer than they appear” on a scooter or car side mirror. The convex mirror shrinks everything, which makes a vehicle behind look smaller — and our brain reads “small” as “far away”. So the warning reminds the driver that the vehicle is actually nearer than it seems. The trade-off is worth it, because the convex mirror also shows a much wider stretch of road behind.

Let us check the idea that distance changes a concave mirror’s image.

Refraction: why light bends

Now we leave mirrors and look at what happens when light passes through a clear material like water or glass, instead of bouncing off it.

Stand a pencil in a glass of water and look from the side. The pencil seems to break and shift at the water surface. The pencil is perfectly straight, of course — so why does it look bent?

The reason is that light bends when it passes from one clear material into another. This bending is called refraction. And the cause of the bending is one simple fact:

Light travels at different speeds in different materials.

It is fast in air, and slower in water and glass.

Why does a change in speed cause bending? Here is a picture that makes it click. Imagine a row of friends walking in a straight line, holding hands, marching from a smooth road onto soft, muddy ground at a slant. The end that reaches the mud first slows down, while the others are still on the fast road. Because one end slows before the rest, the whole line swings round and changes direction. Light does exactly this. When a slanting ray crosses from fast air into slow water, the edge that enters first slows down before the rest, so the ray swings and bends.

Which way does it bend? When light enters a slower material (air into water), it bends towards the normal. Figure 10.7 below shows both the bending ray and the bent-pencil effect it causes.

Tap to zoom

So the pencil looks broken because the light coming from its underwater part bends as it crosses the water surface on the way to your eye. Your brain, assuming light travelled straight, places that part in the wrong spot — and the pencil appears to jump sideways at the surface. The same speed-change is why a swimming pool always looks shallower than it really is.

Lenses: convex and concave

A lens is a piece of clear glass or plastic with curved surfaces. Unlike a mirror, light goes through a lens, and refraction (bending) at its two curved surfaces is what makes it work. There are two kinds, named just like the mirrors:

• A convex lens is thicker in the middle than at the edges. (A magnifying glass is a convex lens. So is the lens inside your own eye.)
• A concave lens is thinner in the middle than at the edges.

What do they do to light? A convex lens bends all the rays inwards so they meet — it converges light. A concave lens bends rays outwards so they spread — it diverges light. Figure 10.8 below shows both.

Tap to zoom

Because a convex lens gathers light, it can do the same Sun trick as a concave mirror: focus sunlight to a tiny bright spot hot enough to burn paper. (Never look at the Sun directly or through a lens — it can harm your eyes.)

And what images do lenses give? You will notice the pattern matches the mirrors closely.

• A convex lens: with the object close, you see it erect and enlarged — this is the magnifying-glass effect. As the object moves farther, the image becomes inverted, first large and then smaller.
• A concave lens: the image is always erect and diminished (smaller), wherever the object is.

Lenses are everywhere: in spectacles that help people see clearly, in cameras (including your phone), in telescopes that bring distant stars closer, and in microscopes that reveal tiny things. Even your eye has a convex lens inside it — an amazing one that changes its own shape so you can focus on a book up close and a building far away.

Let us pull the two lenses together in one view.

Common Mistakes

These are the slip-ups students make most often. Read them once and you will sidestep all three.

Quick Check

Try each one. Each question checks a single idea from the chapter.

Practice Problems

Try each one yourself first. Only then tap to see the full solution.

Easy

Medium

Challenge

Summary

Here is everything you can now explain to a friend:

• We see most things by reflected light — light from a source bounces off the object into our eye. Light travels in straight lines, which we draw as rays.
• A mirror reflects light neatly enough to form an image.
• The two laws of reflection: (1) the angle of incidence equals the angle of reflection, both measured from the normal; (2) the incident ray, the normal and the reflected ray lie in the same plane. These hold for all mirrors.
• A plane mirror gives an image that is erect, the same size, behind the mirror (virtual), and laterally inverted (left-right swapped).
• A concave mirror curves inwards and converges light. Its image is enlarged and erect when the object is close, and inverted when the object is far. Used in dentist’s mirrors, torch and headlight reflectors.
• A convex mirror curves outwards and diverges light. Its image is always small and erect, with a wide view. Used as vehicle side-view mirrors, at road bends, and as shop security mirrors.
• Refraction is the bending of light when it passes between materials, because light has different speeds in them (fast in air, slower in water and glass). It bends towards the normal when entering a slower medium. This is why a pencil in water looks bent.
• A convex lens is thick in the middle and converges light (a magnifying glass, the eye lens). A concave lens is thin in the middle and diverges light. Lenses are used in spectacles, cameras, telescopes, microscopes and our own eyes.

What’s Next

You have just seen how light from the Sun bounces and bends to let us see the world. But the Sun does much more than light our way — its daily journey across the sky has been humanity’s clock and calendar for thousands of years.

In the next chapter, Chapter 11 — Keeping Time with the Skies, you will discover how the movement of the Sun, the Moon and the stars gives us days, months and years — and how a simple shadow can tell the time. Keep that curiosity glowing!