NCERT Exemplar Solutions Class 10 Science Light Reflection and Refraction — Multiple Choice Questions Q11–19

NCERT Exemplar Problems, Class 10 Science — Light: Reflection and Refraction, Multiple Choice Questions 11 to 19. All 9 questions solved.

This is the second half of the unit’s multiple-choice band; Questions 1 to 10 cover the mirror and lens formulae, refractive index and the box questions.

Three of the nine questions here — 14, 16 and 17 — offer four ray diagrams and ask which is correct. They look like the hardest questions on the page and are in fact the most mechanical, provided you do them the right way round: write down what the correct diagram must show, then test the four panels against that list. Trying to spot the right-looking one is how these are got wrong.

The rules those three questions test are worth stating once:

• A ray parallel to the principal axis reflects from a concave mirror through the focus — not through C, not through some point near P.
• A ray passing through the focus of a convex lens emerges parallel to the principal axis. (It is the previous rule run backwards, since light paths are reversible.)
• A ray through a rectangular glass slab bends towards the normal on entering and away on leaving, so it emerges parallel to its original direction but displaced sideways.

Key insight. Every one of these three figure questions has exactly one panel that obeys its rule and three that fail it in different ways — one usually by not bending at all, one by bending through the wrong point, one by bending the wrong way. Naming which rule each wrong panel breaks is what turns a guess into an answer.

Choose the correct answer from the given four options in the following questions:

Question 11

A full length image of a distant tall building can definitely be seen by using

Solution. The word carrying the weight is definitely. The question is not which mirror might show the whole building, but which one is guaranteed to.

A convex mirror always forms a virtual, erect and diminished image of any object, wherever it is — the result of Question 9. Because the image is always shrunk, the whole of a tall building fits into a small mirror every time. That is (b), and it is the only guaranteed answer.

A plane mirror forms an image exactly the same size as the object. To see a whole building in it you would need a mirror at least half the building’s height, which is why (c) fails and why (d) fails with it.

A concave mirror is the least reliable of the three. For a distant object it does form a small real image near the focus, so it can show the whole building — but move the object close and the image becomes magnified, inverted, or virtual. It depends entirely on the distance, and “definitely” rules that out.

The trade-off worth knowing is the one from Question 9: the convex mirror’s diminishing is exactly what gives it a wide field of view, and that is why it is used for rear view mirrors and on blind corners.

Question 12

In torches, search lights and headlights of vehicles the bulb is placed

Solution. All three devices need the same thing: a parallel beam that travels a long way without spreading. The reflector is concave, and Question 1 established how to get a parallel beam from it — put the source at the focus.

The reason is the reversibility of light paths. Rays arriving parallel to the axis converge at the focus; so rays starting at the focus leave parallel. Option (b).

Note the wording: very near to the focus, not exactly at it. That is deliberate and physically honest. A real bulb filament has a finite size, so it cannot all sit at the single point that is the focus, and in practice it is placed as close to the focus as its size allows. Moving it slightly inside or outside the focus is also how some torches let you adjust the beam from a tight spot to a broad flood.

The other options all give a spreading or converging beam. At C, option (d), the light would converge back to C and then diverge — useless for a headlight. Between F and C the reflected rays converge to a distant point. Between P and F they diverge.

Question 13

The laws of reflection hold good for

Solution. The laws of reflection are that the angle of incidence equals the angle of reflection, and that the incident ray, the reflected ray and the normal all lie in the same plane.

Both are stated at the point of incidence, and both are about the relationship between a single ray and the normal at that point. Nothing in either law refers to the shape of the surface.

So they hold for every reflecting surface — plane, concave, convex, and indeed irregular ones. Option (d).

What changes with shape is not the law but the normal. On a plane mirror the normal points the same way everywhere, so parallel rays stay parallel after reflection. On a spherical mirror the normal at each point is along the radius — it points towards the centre of curvature — so it tilts progressively as you move away from the pole, and parallel rays are brought together at the focus.

That is the whole explanation for why curved mirrors converge or diverge light while obeying exactly the same law as a flat one. Even the diffuse reflection from a rough wall obeys it; the surface is simply so irregular that the normals point in all directions.

Question 14

The path of a ray of light coming from air passing through a rectangular glass slab traced by four students are shown as A, B, C and D in Figure 10.5. Which one of them is correct?

Solution. Write down what a correct trace must show before looking at the panels. Light going from air into glass and out again into air must:

1. bend towards the normal on entering the glass, because glass is denser — so the ray becomes steeper inside the slab;
2. travel in a straight line inside;
3. bend away from the normal on leaving, by exactly the same angle;
4. therefore emerge parallel to the incident ray, but displaced sideways.

Step 4 follows from step 3 because the two faces of a rectangular slab are parallel, so the two refractions are equal and opposite. Now test the four.

A shows one straight line all the way through. The ray is not bent at either face, which would only happen if the slab were not there, or if the light struck the surface along the normal. Fails tests 1 and 3.

B bends towards the normal at the top face, runs straight inside, bends away at the bottom face, and the emergent ray is parallel to the incident ray and shifted sideways. All four tests pass. This is the correct trace.

C goes straight into the glass without bending at the first face and then bends on the way out. A ray cannot refract at one parallel face and not the other. The emergent ray is not parallel to the incident one.

D bends at both faces, so it looks more plausible than the others, but the two bends are not equal — the emergent ray is not parallel to the incident ray. That is the subtlest error of the three, and the one to check last.

The sideways shift in B is called the lateral displacement, and it grows with the thickness of the slab and with the angle of incidence.

Question 15

You are given water, mustard oil, glycerine and kerosene. In which of these media a ray of light incident obliquely at same angle would bend the most?

Solution. For the same angle of incidence, the medium that bends light most is the one with the highest refractive index — because a larger $n$ means a smaller angle of refraction, and therefore a bigger change of direction.

$$n = \frac{\sin i}{\sin r}, \qquad \text{so larger } n \Rightarrow \text{smaller } r \Rightarrow \text{more bending}$$

The four refractive indices, from the table in the textbook:

Medium	Refractive index
Water	1.33
Kerosene	1.44
Mustard oil	1.46
Glycerine	1.47

Glycerine has the highest, so it bends the ray most. Option (d).

Refractive index is also inversely related to the speed of light in the medium, $n = c/v$, so the answer can be stated the other way round: light travels slowest in glycerine of these four, and the greater the slowing, the greater the bending.

Water is the odd one out in this list and is worth noticing — it is by far the least refracting of the four, so it bends light the least, which is the answer to the same question asked in reverse.

Question 16

Which of the following ray diagrams is correct for the ray of light incident on a concave mirror as shown in Figure 10.6?

Solution. The incident ray is parallel to the principal axis, and there is exactly one rule for that: a ray parallel to the axis, after reflection from a concave mirror, passes through the principal focus F.

So the test is a single question — where does the reflected ray cross the axis? — and it must be at F.

Fig. A reflects the ray downwards, but it crosses the axis between F and P, short of the focus. Close, and wrong: the crossing point has to be F exactly. This is the panel most often chosen by mistake, because at a glance it looks like D.

Fig. B sends the reflected ray through C, the centre of curvature. A ray through C is a different rule entirely — it is the ray that strikes the mirror along the normal and comes straight back on itself. A parallel ray does not go through C.

Fig. C shows the ray simply retracing its own path back to the left. That happens only when a ray hits the mirror normally, which means travelling along a radius — true for a ray directed at C, not for one parallel to the axis.

Fig. D reflects the ray so that it passes exactly through F. That is the rule, so D is correct.

The reason the rule holds is worth a line: the normal at any point of a spherical mirror is the radius through that point, and for rays close to the axis the geometry makes every parallel ray cross the axis at the midpoint of PC — which is what we call the focus, at $f = R/2$.

Question 17

Which of the following ray diagrams is correct for the ray of light incident on a lens shown in Fig. 10.7?

Solution. The incident ray passes through the focus on the near side of a convex lens, and the rule for that ray is that it emerges parallel to the principal axis.

This is the mirror image of the rule in Question 16, and it holds for the same reason: light paths are reversible. A ray arriving parallel to the axis is brought to the focus; run it backwards and a ray from the focus leaves parallel.

Fig. A shows the emergent ray running parallel to the principal axis. That is the rule, so A is correct.

Fig. B sends the emergent ray up through the focus on the far side. That is the behaviour of a parallel incident ray, not of one through the near focus — the two rules have been swapped.

Fig. C has the emergent ray travelling back to the left, on the same side as the object. Light does not reverse direction on passing through a lens; only a mirror can send it back.

Fig. D carries the ray straight on undeviated. That is what happens to a ray through the optical centre, which is the third standard construction ray — but this ray passes through the focus, not the centre, so it must be deviated.

The three constructions for a convex lens are worth keeping together, because between them they draw every ray diagram in the chapter: parallel in gives focus out; focus in gives parallel out; through the optical centre gives straight on.

Question 18

A child is standing in front of a magic mirror. She finds the image of her head bigger, the middle portion of her body of the same size and that of the legs smaller. The following is the order of combinations for the magic mirror from the top.

Solution. Take the three observations one at a time and match each to the mirror that produces it.

The head is bigger. Only a concave mirror magnifies, and it does so when the object is close to it — nearer than the focus. So the top section is concave.

The middle is the same size. A plane mirror always gives an image the same size as the object. So the middle is plane.

The legs are smaller. A convex mirror always diminishes, whatever the distance. So the bottom is convex.

Reading from the top down: concave, plane, convex — option (c).

Two of the wrong options can be eliminated almost without thought. Both (b) and (d) put convex at the top, and convex mirrors cannot enlarge anything; (a) puts plane at the top, which cannot enlarge either. Only (c) has a magnifying mirror where the magnification is reported.

The question is a neat summary of the whole chapter’s mirror behaviour, which is worth having in one place:

Mirror	Image
Concave, object near	Virtual, erect, magnified
Plane	Virtual, erect, same size
Convex	Virtual, erect, diminished

Question 19

In which of the following, the image of an object placed at infinity will be highly diminished and point sized?

Solution. An object at infinity sends rays that arrive parallel to one another. What each device does with a parallel beam is precisely what defines its focus — and every one of the four brings that beam to a focal point.

• Concave mirror — converges the rays to a real point image at F, in front of the mirror.
• Convex lens — converges them to a real point image at F, on the far side.
• Convex mirror — the reflected rays diverge, but they appear to come from a point behind the mirror: a virtual point image at F.
• Concave lens — the same, a virtual point image at F on the incoming side.

In all four cases the image is a point, and therefore highly diminished. The difference between them is whether the image is real or virtual and which side of the device it lies on — not whether it is point sized.

So the answer is (d): all four.

The reason the options are phrased with “only” is that each of (a), (b) and (c) is a true statement that is not the whole truth. A concave mirror really does form a point image of a distant object; so the temptation is to stop there. The question asks in which of the following, and the answer is in all of them.

This is also the basis of the standard method for measuring focal length: focus the image of a distant object — the Sun, or a far building — and the distance from the device to the sharp image is $f$. Questions 10 and 26 both use it.

Common mistakes

• Answering a “definitely” question with a “sometimes” device, in Question 11. A concave mirror can show a whole distant building; a convex mirror always does. When a question says definitely or always, the answer is the device whose behaviour does not depend on distance.
• Sending the reflected ray through C in Question 16. A ray parallel to the axis reflects through F. Through C is the rule for a ray that arrives along a radius and comes straight back.
• Confusing the two lens rules in Questions 16 and 17. Parallel in gives focus out; focus in gives parallel out. Fig. B in Question 17 is the first rule applied to the second situation.
• Accepting a trace that bends at both faces, in Question 14. Panel D bends twice and is still wrong, because the emergent ray is not parallel to the incident one. The parallel-faces argument is what forces the two bends to be equal.
• Choosing “only” options in Question 19. All four devices form a point image of an object at infinity; three of the options are true statements that are incomplete.
• Putting the bulb at the centre of curvature in Question 12. At C the light converges back on itself. A parallel beam needs the source at the focus.
• Thinking curved mirrors obey a modified law of reflection, in Question 13. The law is identical; what changes is the direction of the normal, which on a sphere points along the radius and therefore tilts from point to point.
• Reading a refractive index table as a density table, in Question 15. Optical density and mass density are different things — water is denser than kerosene by mass and refracts less.

Practise next

• Exemplar Multiple Choice Questions Q1–10 — the mirror and lens formulae, refractive index and the two box questions.
• Exemplar Short and Long Answer Questions — where the ray diagrams of Questions 16 and 17 have to be drawn from scratch for every object position.
• NCERT textbook Chapter 9 — Light: Reflection and Refraction for the end-of-chapter exercise on image formation and the sign convention.
• Textbook activities for the glass-slab tracing of Question 14, which is done on paper with pins there rather than described.