NCERT Exemplar Class 10 Science Solutions Chapter 10 Light Reflection and Refraction

Question:2

A 10 mm long awl pin is placed vertically in front of a concave mirror. A 5 mm long image of the awl pin is formed at 30 cm in front of the mirror. The focal length of this mirror is
(a) – 30 cm
(b) – 20 cm
(c) – 40 cm
(d) – 60 cm

Answer: (b)
Given,
Size of object, O = + 10.0 mm = + 1.0 cm
Size of image size, I = 5.0 mm = 0.5 cm
Image distance = − 30 cm (as image is real)
Let, object distance = u
Focal length= f
Magnification m = $\frac{I}{O}$
Magnification is also given as,$m=-\frac{v}{u}$
Therefore, $\frac{I}{O}=\frac{-v}{u}$
$\frac{0.5}{1.0}=-\frac{30}{u}$
Therefore, $u=-60\; cm$
Focal length is given by $\frac{1}{f}=\left ( \frac{1}{v} \right )+\left ( \frac{1}{u} \right )$
or, $\frac{1}{f}=-\frac{3}{60}$
Therefore, $f= -20\; cm$

Question:3

Under which of the following conditions a concave mirror can form an image larger than the actual object?
(a) When the object is kept at a distance equal to its radius of curvature
(b) When the object is kept at a distance less than its focal length
(c) When the object is placed between the focus and the centre of curvature
(d) When the object is kept at a distance greater than its radius of curvature

Answer: (c)
When an object is placed between the focus and centre of curvature, a concave mirror can form an image larger than the actual object.

Question:4

Figure 10.1 shows a ray of light as it travels from medium A to medium B. The Refractive index of medium B relative to medium A is
(a) $\sqrt{3}/\sqrt{2}$
(b) $\sqrt{2}/\sqrt{3}$
(c) ${1}/\sqrt{2}$
(d) $\sqrt{2}$

Answer: (a)
Refractive index of B with respect to A $=\frac{\sin\; i}{\sin\; r}$
$=\frac{\sin\; 60^{o}}{\sin\; 45^{o}}$
$=\frac{\sqrt{3}}{\sqrt{2}}$

Question:5

A light ray enters from medium A to medium B as shown in Figure 10.2. The refractive index of medium B relative to A will be
(a) greater than unity
(b) less than unity
(c) equal to unity
(d) zero

Answer: (a)
Since a ray of light bends towards the normal when it goes from medium A to medium B, therefore, medium A is rarer and medium B is denser. The speed of light in a rarer medium (v₁) is greater than the speed of light in a denser medium (v₂). Hence, n_BA>1.

Question:6

Beams of light are incident through the holes A and B and emerge out of box through the holes C and D respectively as shown in the Figure10.3. Which of the following could be inside the box?

(a) A rectangular glass slab
(b) A convex lens
(c) A concave lens
(d) A prism?

Answer: (a)
A rectangular glass slab refracts and then re-refracts the rays when incident rays fall perpendicularly at the point of incidence on a rectangular glass slab. A rectangular glass slab causes the lateral displacement of a ray of light passing through it. However, the incident ray and emergent ray are parallel to each other.

Question:7

A beam of light is incident through the holes on side A and emerges out of the holes on the other side of the box as shown in figure. Which of the following could be inside the box?

(a) Concave lens
(b) Rectangular slab
(c) prism
(d) Convex lens

Answer: (d)
The incident rays are parallel, and the emergent rays are diverging. A concave lens is diverging in nature, but the answer is a convex lens, as you can see, ray 10, which is at the top, comes last after emerging out of the box, which means it converges first, then diverges as shown in the figure below.

Question:8

Which of the following statements is true?
(a) A convex lens has 4 dioptre power having focal length 0.25 m.
(b) A convex lens has – 4 dioptre power having focal length 0.25 m.
(c) A concave lens has 4 dioptre power having focal length 0.25 m.
(d) A concave lens has – 4 dioptre power having focal length 0.25 m

Answer: (a)
A convex lens has positive power and positive focal length.
$ P=\frac{1}{f}$
$ \therefore f=\frac{1}{P}=\frac{1}{4}=0.25\; m$

Question:9

Magnification produced by a rear-view mirror fitted in vehicles.
(a) is less than one
(b) is more than one
(c) is equal to one
(d) can be more than or less than one depending upon the position of the object in front of it.

Answer: (a)
A rear-view mirror is a convex mirror, which always forms an image whose size is less than the size of the object. A convex mirror always forms a smaller image. Therefore, the magnification of the rear-view mirror is always less than 1.

Question:10

Rays from sun converge at a point 15 cm in front of a concave mirror. Where should an object be placed so that size of its image is equal to the size of the object?
(a) 15 cm in front of the mirror
(b) 30 cm in front of the mirror
(c) between 15 cm and 30 cm in front of the mirror.
(d) more than 30 cm in front of the mirror.

Answer: (b)
Here, the focal length of the concave mirror, f = -15 cm
Radius of curvature of the mirror, R = 2f = -30 cm.
In the case of a concave mirror, the size of the image is equal to the size of the object if the object is placed at the centre of curvature. The distance of the centre of curvature from the mirror = radius of curvature of the mirror. When an object is placed at R, the image formed is of the same size as that of the object. The image is formed at R, and it is inverted.

Question:11

A full-length image of a distance tall building can definitely be seen by using
(a) concave mirror
(b) convex mirror
(c) plane mirror
(d) both concave as well as plane mirror.

Answer: (b)
The field of convex mirrors is more than any other type of mirror. A convex mirror forms the full length of a distant, tall object, irrespective of the position of the object. However, a plane mirror forms a full-size image of the object if the size of the plane mirror is half the size of the object. A concave mirror forms a full-size image of the object if the object is far away from it.

Question:12

In torches, search lights and headlights of vehicles the bulb is placed
(a) between the pole and the focus of the reflector
(b) very near to the focus of the reflector
(c) between the focus and center of curvature of the reflector
(d) at the center of curvature of the reflector

Answer: (b)
Concave mirrors are used in headlight reflectors and search lights. When the source of light is placed at the focus, the reflected light appears like a beam.

Question:13

The laws of reflection hold good for
(a) plane mirror only
(b) concave mirror only
(c) convex mirror only
(d) all mirrors irrespective of their shape

Answer: (d)
The laws of reflection hold good for all mirrors, irrespective of their shape.

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 the figure. Which one of them is correct?

(a) A
(b) B
(c) C
(d) D

Answer: (b)
When light passes from air to glass, it bends towards the normal, and when light passes from glass to air, it bends away from the normal. A Glass slab causes the lateral displacement of a ray of light falling on it. However, the incident ray and emergent ray are parallel to each other.

Question:15

You are given water, mustard oil, glycerin and kerosene. In which of these media, a ray of light incident obliquely at same angle would bend the most?
(a) Kerosene
(b) Water
(c) Mustard Oil
(d) Glycerin

Answer: (d)
The refractive indices of water, kerosene, mustard oil and glycerin are 1.33, 1.44, 1.46 and 1.47, respectively. The ray would bend the most when it goes from a rarer medium (say, air) to a denser medium. Since the refractive index of glycerin is the highest among all these media, glycerin is the densest medium.

Question:16

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

(a) Fig. a
(b) Fig. b
(c) Fig. c
(d) Fig. d

Answer: (d)
Any ray of light parallel to the principal axis passes through the focus (F) after reflecting from the concave mirror.

Question:17

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


(a) Fig. a
(b) Fig. b
(c) Fig. c
(d) Fig. d

Answer: (a)
A ray of light passing through the focus of a lens travels parallel to the principal axis after refracting through the lens.

Question:18

A girl 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 order of combinations for the magic mirror from the top:
(a) Plane, convex and concave
(b) Convex, concave and plane
(c) Concave, plane and convex
(d) Convex, plane and concave

Answer: (c)
A concave mirror forms a magnified (enlarged) image of the object if the object is placed close to the concave mirror (i.e., a distance less than its focal length). A plane mirror always forms an image of the same size as the object.

Question:19

In which of the following, the image of an object placed at infinity will be highly diminished and point sized?
(a) Concave mirror only
(b) Convex mirror only
(c) Convex lens only
(d) Concave mirror, convex mirror, concave lens and convex lens.

Answer: (d)
From ray diagrams, we can see that in a Concave mirror, a convex mirror, a concave lens and a convex lens, the image of an object placed at infinity will be highly diminished and point-sized.

Question:21

Why does a light ray incident on a rectangular glass slab immersed in any medium emerges parallel to itself? Explain using a diagram.

Answer:
When a light ray enters a denser medium from a rarer medium, it bends towards the normal. Again, when this ray exists in the second medium and enters the first, it ends away from the normal. In this case, the extent of bending of the ray at the opposite faces is the same; this is the reason why the emergent ray is parallel to the incident ray.

Question:22

A pencil when dipped in water in a glass tumbler appears to be bent at the interface of air and water. Will the pencil appear to be bent to the same extent, if instead of water, we use liquids like, kerosene or turpentine. Support your answer with reason.

Answer:
The bending of light takes place because of refraction. Refraction depends on the refractive indices of the medium. A pencil dipped in water appears to be bent at the interface of air and water due to the refraction of light. The refraction of light occurs because the speed of light changes when light travels from one medium to another. The pencil will not appear to be bent to the same extent when it is dipped in kerosene or turpentine. This is because the refractive index of kerosene or turpentine is greater than the index of water, and hence the speed of light (v = c/n) is less in kerosene or turpentine as compared to in water.

Question:23

How is the refractive index of a medium related to the speed of light? Obtain an expression for the refractive index of a medium with respect to another in terms of the speed of light in these two media.

Answer:
The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values.
n = c/v (where n: refractive index, c = speed of light, v: velocity of light in that medium)
Refractive index of one medium in relation to a second medium is given by the ratio of the speed of light in the second medium to the speed of light in the first medium.
$n_{21}=\frac{v_{1}}{v_{2}}$

Question:24

Refractive index of diamond with respect to glass is 1.6 and absolute refractive index of glass is 1.5. Find out the absolute refractive index of diamond.

Answer :
The absolute refractive index of a medium shows the ratio of the speed of light in air to the speed of light in that medium. Let us assume c is the speed of light in air, v₁ is the speed of light in glass, and v₂ is the speed of light in diamond.
R_dg =1.6 ----(1)
Absolute refractive index of glass,
R_ga =1.5 -----(2)
Multiplying equations (1) and (2),
$R_{da}\times R_{ga}=1.6\times 1.5=2.4$
So, the absolute refractive index of diamond = 2.4

Question:25

A convex lens of focal length 20 cm can produce a magnified virtual as well as real image. Is this a correct statement? If yes, where shall the object be placed in each case for obtaining these images?

Answer:
The statement is correct.
When an object is placed between F and F₂ of a convex lens, its enlarged, inverted and real image is formed beyond 2F₂, i.e., on the other side of the lens. So, for this, we need to place the object between 20cm and 40cm from the lens.
When an object is placed between F and O of a convex lens, its enlarged, erect and virtual image is formed beyond F₂, i.e., on the same side of the lens. So, for this, we need to place the object at a distance less than 20 cm from the lens.

Question:26

Sudha finds out that the sharp image of the window pane of her science laboratory is formed at a distance of 15 cm from the lens. She now tries to focus the building visible to her outside the window instead of the window pane without disturbing the lens. In which direction, will she move the screen to obtain a sharp image of the building? What is the approximate focal length of this lens?

Answer:
A real image can be obtained on the screen. Therefore, the lens used is a convex lens as it forms a real as well as a virtual image. The distance of the real image formed by a convex lens from the lens decreases as the object distance from the lens increases. Hence, the screen has to be moved towards the lens to obtain a sharp image of the building.
Approximate focal length of the lens = 15 cm. The rays of light from the window pane are considered to come from infinity. These rays of light are focused by the convex lens at its focus (i.e. on the screen).

Question:27

How are power and focal length of a lens related? You are provided with two lenses of focal length 20 cm and 40 cm respectively. Which lens will you use to obtain more convergent light?

Answer:
The power of a lens is reciprocal to its focal length. So, a smaller focal length means more power. Out of the given lenses, the lens with a 20 cm focal length has more power than the lens with a 40 cm focal length. The lens with higher power should be used to obtain more convergent light.
The lens of focal length 20 cm or power 5.0 D will be used to have more convergent light. This is because the lens of a small focal length or large power strongly converges the parallel beam of light.

Question:28

Under what condition in an arrangement of two plane mirrors, incident ray and reflected ray will always be parallel to each other, whatever may be angle of incidence. Show the same with the help of diagram.

Answer:
When two plane mirrors are at right angles to each other, the incident ray and reflected ray will always be parallel to each other, whatever the angle of incidence. From the diagram, for any value of i, the deviation will always be 180 degrees. This means that the incident ray and reflected ray will always be parallel, irrespective of the value of the angle of incidence.

Question:29

Draw a ray diagram showing the path of rays of light when it enters with oblique incidence (i) from air into water; (ii) from water into air.

Answer:
(i) Ray diagram showing the path of rays of light when it enters with oblique incidence from air into water

(ii) From a denser medium to a rarer medium, the light ray bends away from the normal.

Question:31

Draw ray diagrams showing the image formation by a convex lens when an object is placed
(a) between optical centre and focus of the lens
(b) between focus and twice the focal length of the lens
(c) at twice the focal length of the lens
(d) at infinity
(e) at the focus of the lens

Answer:
(a) between the optical centre and the focus of the lens

(b) between the focus and twice the focal length of the lens

(c) at twice the focal length of the lens

(d) at infinity

(e) At the focus of the lens

Question:32

Write laws of refraction. Explain the same with the help of ray diagram, when a ray of light passes through a rectangular glass slab.

Answer:

Laws of refraction:

1. The incident ray, the normal to any refracting surface at the point of incidence, and the refracted ray all lie in the same plane called the plane of incidence or plane of refraction.
2. The ratio of the sine of the angle of incidence to the angle of refraction is always constant.

$\frac{\sin i}{\sin r}=\mathrm{constant}$

$\frac{\sin i}{\sin r}=\frac{\mu _{2}}{\mu _{1}}=\frac{v_{1}}{v_{2}}=\frac{\lambda_{1}}{\lambda_{2}}$
or
$ \mu _{1} \sin i=\mu _{2} \sin r $
$\frac{\sin(i)}{ \sin(r)}= \mu _{21}$ = refractive index of the second medium with respect to the first medium.
For a glass slab as shown in the figure

i = angle of incidence
r₁ = angle of reflection
$\frac{sin i}{sin r_1}=\frac{\mu_g}{\mu_{air}}$

Question:33

Draw ray diagrams showing the image formation by a concave lens when an object is placed
(a) at the focus of the lens
(b) between focus and twice the focal length of the lens
(c) beyond twice the focal length of the lens

Answer :
(a) at the focus of the lens

(b) between the focus and twice the focal length of the lens

(c) beyond twice the focal length of the lens

Question:34

Draw ray diagrams showing the image formation by a convex mirror when an object is placed
(a) at infinity
(b) at finite distance from the mirror

Answer :
(a) at infinity

(b) at a finite distance from the mirror

Question:35

The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is three times the size of the flame and the distance between lens and image is 80 cm, at what distance should the candle be placed from the lens? What is the nature of the image at a distance of 80 cm and the lens?

Answer :
The image is obtained on the screen, so it is real.
Therefore, magnification, m = –3,
v = 80 cm
Now, $m=\frac{v}{u}$
Therefore,
$-3=\frac{80}{u}$

$u=\frac{-80}{3}cm$

$f=\left ( \frac{1}{v} \right )-\left ( \frac{1}{u} \right )=\left ( \frac{1}{80} \right )+\left ( \frac{3}{80} \right )=\frac{1}{20}$

$f=20\; cm$

The lens is convex, and the image formed at 80 cm from the lens is real and inverted.

Question:36

Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to 1/3rd of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?

Answer:

Using,
m = - v/u = h_i/h_o
⇒ - v/u = 1/3
⇒ u = - 3v
Using the mirror formula,
1/v + 1/u = 1/f, we get
when f = + 20 cm
⇒ 1/v - 1/3v = 1/20
⇒ 3 - 1/3v = 1/20
⇒ 2/3v = 1/20
⇒ 3v = 2 × 20
⇒ v = 2 × 30/3
⇒ v = 40/3 .. (i)
u = - 3v
By putting the v value, we get
⇒ u = - 3 × 40/3
⇒ u = - 40 cm.
Object Distance = - 40 cm
If we take f = - 20 cm, the value of u will be + 40 cm, which is not possible.
m = - v/v
⇒ m = - 40/3/- 40
⇒ m = + 1/3
⇒ m = 0.33 cm
This implies that the nature of the image is erect and diminished.
Nature of Image = Convex Mirror.

Question:37

Define power of a lens. What is its unit? One student uses a lens of focal length 50 cm and another of –50 cm. What is the nature of the lens and its power used by each of them?

Answer:
P = 1 / f, where f is in meters.
The unit of power is Diopter. The lens is convex in the first case and concave in the second case. Power of lens (first student) = +2 diopter
Power of lens (second student) = -2 diopter

Question:38

A student focused the image of a candle flame on a white screen using a convex lens. He noted down the position of the candle screen and the lens as under
Position of candle = 12.0 cm
Position of convex lens = 50.0 cm
Position of the screen = 88.0 cm
(i) What is the focal length of the convex lens?
(ii) Where will the image be formed if he shifts the candle towards the lens at a position of 31.0 cm?
(iii) What will be the nature of the image formed if he further shifts the candle towards the lens?
(iv) Draw a ray diagram to show the formation of the image in case (iii) as said above.

Answer:

Answer :
(i) Focal length = 38 ÷ 2 = 19 cm
(ii) object distance u = 50 – 31 = 19 cm
In this case, object distance = focal length
This means that images is formed at infinity.
(iii) The image formed will be virtual and erect.
(iv)