Light – Reflection and Refraction: Class 10 Science · Chapter 9

During a power cut on a moonless night, your room seems to vanish. The bed and the cupboard are still there, yet you cannot see them. Light a candle and they come back. We see a thing only when light travels from it into our eyes. The Sun, a bulb or a candle flame makes its own light; a book, a wall or a face sends back part of the light that falls on it. Light can also pass through clear glass and water, which is why a window lets you see the street.

Watch a torch beam in a dusty room, or a shaft of sunlight through a gap in a curtain: it runs straight. A small bulb casts a shadow with sharp edges, because light does not curve round an object into the space behind it. We draw this straight path as a line with an arrow and call it a ray. In this chapter, rays are all we need to explain mirrors, lenses and the bending of light. The same ideas lead on to the human eye and the rainbow in the next chapter.

9.1 Reflection of Light

Smooth, shiny surfaces such as a mirror, a polished steel plate or still water send back most of the light that reaches them. You met the two rules of reflection in earlier classes. They apply to every surface, flat or curved, provided we measure angles from the normal: the line drawn at right angles to the surface at the point where the ray strikes it.

So a plane mirror gives an image that is virtual (no light actually reaches the spot behind the glass), erect and the same size as the object. It sits exactly as deep behind the glass as the object stands in front, and it is laterally inverted: your right hand appears as the image's left hand. This is why the word AMBULANCE is painted back to front on the bonnet of an ambulance. A driver ahead reads it the right way round in the rear-view mirror.

What happens when the mirror is curved? Try the activity below before reading on.

The two sides of the katori are curved mirrors. The most useful curved mirrors have a reflecting surface that is part of a sphere, so they are called spherical mirrors.

9.2 Spherical Mirrors

Picture a hollow glass ball, silvered and cut into pieces. Each piece is a spherical mirror. If the reflecting face is the inner, caved-in one, which faces the centre of the sphere, the piece is a concave mirror (अवतल दर्पण). If the reflecting face bulges outwards, it is a convex mirror (उत्तल दर्पण). The inside of a steel spoon is roughly concave and its back is roughly convex. In diagrams we draw a spherical mirror as a curved line and hatch its back, the side that does not reflect.

A few names let us describe these mirrors exactly (Fig. 9.2).

Sunlight arrives as rays parallel to one another. When rays parallel to the principal axis strike a concave mirror, they all reflect through a single point on the axis. When they strike a convex mirror they spread out, but traced backwards they seem to come from a single point behind the mirror (the last two steps of Fig. 9.2).

The width of the reflecting surface is its aperture. We deal only with mirrors whose aperture is small compared with their radius of curvature. For these, the focus lies exactly halfway between the pole and the centre of curvature, so the radius of curvature is twice the focal length:

9.2.1 Image Formation by Spherical Mirrors

A plane mirror always gives the same kind of image. A concave mirror does not: its image may form in front of the mirror or behind it, and may be larger or smaller, upright or upside down, depending on where the object is. Two words describe every image.

9.2.2 Representation of Images Formed by Spherical Mirrors Using Ray Diagrams

Every point of an object sends rays in all directions, and the mirror forms an image of each point. To find where the image of the tip of an object lies, we do not need all those rays. We follow two rays whose paths after reflection we can predict and see where they cross. Four rays are especially easy to follow (Fig. 9.3).

1. A ray parallel to the principal axis reflects through F (concave mirror), or reflects so that it seems to come from F (convex mirror).
2. A ray through F (concave mirror), or one heading towards F (convex mirror), reflects parallel to the principal axis. This is the first rule run backwards.
3. A ray through C (concave mirror), or one heading towards C (convex mirror), meets the mirror along the normal and returns along the same line.
4. A ray that strikes the pole reflects at an equal angle on the other side of the principal axis, because the axis is the normal at P.

None of these is a new law: each one is the law of reflection applied at a convenient point. Use any two of them to locate an image; a third ray is a useful check.

(a) Image formation by a concave mirror

Fig. 9.4 uses the parallel ray and the ray through (or from) F for each object position in Table 9.3. Step through it and notice the pattern. As the object moves in towards F, the real image runs away from the mirror and grows. Once the object is inside F, the reflected rays no longer meet in front, and the image jumps behind the mirror.

In the explorer, tap each position button for the concave mirror and check the status line against Table 9.3. Then slide the object slowly through F and watch the image disappear to infinity on one side and reappear behind the mirror.

Uses of concave mirrors. Each use matches a row of Table 9.3:

• Solar cookers and solar furnaces: a large concave reflector brings sunlight to its focus, where the concentrated energy cooks food or even melts metal (the first row).
• Dentists' mirrors: a small concave mirror held close to a tooth shows a magnified view of it.
• Shaving and make-up mirrors: your face is closer than F, so you see an enlarged, upright image (the last row).
• Torches, searchlights and vehicle headlights: the bulb sits at F, so the reflected light leaves as a strong parallel beam (the at-F row).

(b) Image formation by a convex mirror

A convex mirror spreads light out, so the reflected rays never meet in front of it. Wherever the object is, the rays only seem to come from a point behind the mirror, between P and F. So the image is always virtual, upright and smaller than the object. Only two cases need a diagram: an object very far away and an object at an ordinary distance (Fig. 9.6).

Uses of convex mirrors. Look at the wing mirror of a bus or a scooter: it bulges. A driver needs two things from it. First, an upright image at every distance, so that traffic behind never appears upside down. Second, a wide view of the road behind: the bulge gathers light from a much wider angle than a flat mirror of the same size. The same mirrors guard sharp bends on ghat roads and the corners of shops. The catch is that vehicles look smaller, so they seem farther away than they really are.

9.2.3 Sign Convention for Reflection by Spherical Mirrors

To use a formula for mirrors we must say which way each distance points. We use the New Cartesian sign convention. It treats the principal axis as the x-axis of a graph, with the origin at the pole (Fig. 9.8):

1. Place the object to the left of the mirror, so that light travels from left to right towards the mirror.
2. Measure every distance along the principal axis from the pole.
3. Distances measured to the right of the pole (along +x) are positive; distances to the left (along −x) are negative.
4. Heights measured upwards from the principal axis (+y) are positive.
5. Heights measured downwards from the principal axis (−y) are negative.

Two shortcuts follow. The object distance $u$ is always negative, because the object is always on the left. A concave mirror's focus is in front of it, so its $f$ (and $R$) is negative; a convex mirror's focus is behind it, so its $f$ is positive.

9.2.4 Mirror Formula and Magnification

Three lengths, all measured from the pole, describe a mirror set-up: the object distance $u$, the image distance $v$, and $f$ for the focus. The mirror formula links them:

One formula covers every case, concave or convex, object near or far, as long as each quantity goes in with its sign. Never guess a sign: decide it from the convention, put it in, and let the algebra tell you the sign of the answer.

Magnification. The magnification (आवर्धन) $m$ says how many times taller the image is than the object. With $h$ the object height and $h^{\mathrm{\prime }}$ the image height:

It can also be found from the two distances:

The object stands on the axis pointing up, so $h$ is positive. Then the sign of $m$ tells you the nature of the image. A negative $m$ means the image hangs below the axis: it is inverted, and real. A positive $m$ means it is upright, and virtual. The size of $m$ tells you the rest: $\mathrm{\mid }m\mathrm{\mid }>1$ enlarged, $\mathrm{\mid }m\mathrm{\mid }=1$ same size, $\mathrm{\mid }m\mathrm{\mid }<1$ diminished.

9.3 Refraction of Light

Look down into a clear swimming pool and the bottom seems nearer than it is; people who jump in expecting shallow water get a shock. A straw in a glass of nimbu-paani looks broken at the surface. A glass paperweight seems to lift the words beneath it, and a fish in a round bowl looks bigger when you view it from the side.

In each case light crosses from one transparent material into another, from water or glass into air, before it reaches your eye. Light from the part of the straw under water leaves the surface in a new direction. Your brain assumes light travels in straight lines, so it places that part of the straw in the wrong spot. The effect is stronger for some pairs of materials than for others: a straw in cooking oil looks bent by a different amount. This change of direction is called refraction (अपवर्तन).

9.3.1 Refraction through a Rectangular Glass Slab

A rectangular glass slab is the simplest place to trace a refracted ray, because its two long faces are flat and parallel. The classic method uses pins.

The bending at the two faces is equal and opposite. Because the faces are parallel, the second face exactly undoes what the first one did to the direction. So the ray leaves in its original direction, displaced a little to one side. The thicker the slab and the more slanted the ray, the bigger this lateral (sideways) shift. A ray that meets the slab along the normal goes straight through without bending.

Why does light bend at all? Its speed changes as it crosses from one medium into another: light travels more slowly in glass than in air. Picture a row of soldiers marching at a slant from a road onto sand. The end of the row that reaches the sand first slows down first, so the whole row swings round to a new direction. Experiments show that refraction obeys two laws.

This constant has a name, the refractive index, and it is the subject of the next section.

9.3.2 The Refractive Index

Some pairs of media bend light a lot and others only a little. The refractive index (अपवर्तनांक) puts a number on this, and the number is tied to the speed of light. Nothing beats light in empty space, about $3\times {10}^8\mathrm{m}\mathrm{/}\mathrm{s}$. Air slows it by only about 0.03 %, but water and glass slow it by a quarter to a third.

Let light cross from medium 1, where its speed is $v_1$, into medium 2, where its speed is $v_2$. Dividing the first speed by the second gives $n_{21}$, the refractive index of medium 2 relative to medium 1:

Swap the media and the ratio turns upside down:

When the first medium is vacuum (air is close enough that we treat it the same way), the ratio is the absolute refractive index of the medium, usually just called its refractive index $n_m$. With $c$ the speed of light in vacuum and $v$ its speed in the medium:

For water $n=1.33$: in the time light covers 1.33 m in air, it covers only 1 m in water. Crown glass has $n=1.52$. You need not memorise such values, but you should be able to use them. Fig. 9.11 sends the same ray into three materials: the larger the refractive index, the more sharply the ray turns towards the normal.

9.3.3 Refraction by Spherical Lenses

A watch repairer fits a small magnifier into one eye; reading glasses make print look bigger; a phone camera hides a stack of tiny lenses. A lens (लेंस) is a clear piece of glass or plastic shaped so that at least one of its faces is curved like part of a sphere; the other face may be flat.

A lens that is thicker in the middle than at the edges is a convex lens. It brings parallel rays together, so it is also called a converging lens. A lens that is thinner in the middle is a concave lens; it spreads parallel rays apart and is called a diverging lens. In this chapter, 'convex lens' means a lens with both faces bulging outwards, and 'concave lens' one with both faces curving inwards.

Each curved face is part of a sphere, so a lens has two centres of curvature, $C_1$ and $C_2$. The line through them is the principal axis. The central point of the lens on this axis is its optical centre O. The diameter of the lens is its aperture. We study only thin lenses with small apertures, whose two centres of curvature are equally far from O.

Rays parallel to the principal axis, after passing through a convex lens, meet at a point on the axis on the far side: the principal focus. After a concave lens, they spread out as if they came from a point on the axis on the side they entered. Light can enter a lens from either side, so every lens has two principal foci, $F_1$ and $F_2$, one on each side and equally far from O. That distance is the focal length $f$ of the lens.

9.3.4 Image Formation by Lenses

Like a concave mirror, a convex lens forms different kinds of image depending on where the object is. We can find them with a bench experiment much like Activity 9.3.

9.3.5 Image Formation in Lenses Using Ray Diagrams

Ray diagrams for lenses work just like those for mirrors, except that the rays pass through instead of bouncing back. For a thin lens we draw all the bending at the central line of the lens. Any two of these three rays locate an image (Fig. 9.13):

1. A ray parallel to the principal axis passes through $F_2$ after a convex lens, or spreads out as if it came from $F_1$ after a concave lens.
2. A ray through $F_1$ of a convex lens, or one heading towards $F_2$ of a concave lens, comes out parallel to the principal axis.
3. A ray through the optical centre O goes straight on without bending.

Fig. 9.14 applies the parallel ray and the ray through O to every row of Table 9.8 and Table 9.9. Then use the lens explorer: drag the object across $2F_1$ and $F_1$ and watch the image change side and character.

9.3.6 Sign Convention for Spherical Lenses

Lenses use the same New Cartesian convention as mirrors, with one change: every distance is measured from the optical centre O instead of the pole. Light still comes from the left, so $u$ is negative. The focus that matters for a convex lens, $F_2$, is on the right, so its focal length is positive; a concave lens has a negative focal length. Heights above the axis are positive and heights below it negative, as before.

9.3.7 Lens Formula and Magnification

The lens formula links $u$, $v$ and $f$ for a lens. Notice the minus sign, which is different from the mirror formula:

As with mirrors, one formula serves both kinds of lens and every object position, provided the signs come from the convention. Magnification is defined exactly as for mirrors:

But its link with the distances has no minus sign:

Why the difference? A real image from a lens forms on the right ($v$ positive) while the object is on the left ($u$ negative), so $v\mathrm{/}u$ is already negative for a real, inverted image. For a mirror, a real image forms on the same side as the object, so an extra minus sign is needed to make $m$ negative. The meaning is the same for both: negative $m$ means real and inverted, positive $m$ means virtual and erect.

9.3.8 Power of a Lens

Hold a thick and a thin magnifying glass in sunlight. The thick one brings the light to a point much nearer to itself, because it turns the rays more sharply. Concave lenses behave alike: the shorter the focal length, the harder they spread light. The power (क्षमता) of a lens measures this bending ability. It is the reciprocal of the focal length:

With $f$ in metres, power is in dioptres (D), and $1\mathrm{D}=1{\mathrm{m}}^{-1}$: a lens that focuses parallel light one metre away has a power of one dioptre. A convex lens has positive power and a concave lens negative power, following the sign of $f$ (Fig. 9.16).

Opticians write prescriptions in dioptres. A prescription of $+1.25\mathrm{D}$ means a convex lens with $f=1\mathrm{/}1.25=+0.80\mathrm{m}$. One of $-4.0\mathrm{D}$ means a concave lens with $f=-0.25\mathrm{m}$, that is, $25\mathrm{c}\mathrm{m}$.