# ICSE Solutions for Chapter 7 Reflection of Light Class 9 Physics Selina Publisher

Exercise 7(A)

1. What do you mean by reflection of light?

The return of light into the same medium after striking a surface is called reflection.

2.State which surface of a plane mirror reflects most of the light incident on it: the front smooth surface or the back silvered surface.

Black silvered surface reflects most of the light incident on it.

3. Explain the following terms:

(a) Plane mirror,

(b) Incident ray,

(c) Reflected ray,

(d) Angle of incidence and

(e) Angle of reflection.

Draw diagram/diagrams to show them.

(a) Plane mirror: Plane mirror is a highly polished and smooth reflecting surface made from a clear plane glass sheet, usually thin and silvered with suitable reflecting abrasive (for example, mercury) on one side. Once this pasting is done, then the glass becomes opaque but due to the reflecting property of the abrasive, the plane glass sheet becomes a plane glass reflector or a plane glass mirror.

(b) Incident ray: The light ray striking a reflecting surface is called the incident ray.

(c) Reflected ray: The light ray obtained after reflection from the surface, in the same medium in which the incident ray is travelling, is called the reflected ray.

(d) Angle of incidence: The angle which the incident ray makes with the normal at the point of incidence is called the angle of incidence. It is denoted by the letter i.

(e) Angle of reflection: The angle which the reflected ray makes with the normal at the point of incidence is called the angle of reflection. It is denoted by the letter r.

4. With the help of diagrams, explain the difference between the regular and irregular reflection.

Regular reflection occurs when a beam of light falls on a smooth and polished surface and irregular reflection occurs when a beam of light falls on a rough surface. Since the surface is uneven, from different points light rays get reflected in different directions and give rise to irregular reflection.

5. Differentiate between the reflection of light from a plane mirror and that from a plane sheet of paper.

Reflection of light from a plane mirror is regular reflection and reflection of light from plane sheet of paper is irregular reflection of light.

6. State the two laws of reflection of light.

Laws of reflection:

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, lie in the same plane.

7. State the law of reflection and describe an experiment to verify them.

Laws of reflection :

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, so in the same plane.

Experiment to verify the laws of reflection :

Fix a white sheet of paper on a drawing board and draw a line MM1  as shown in figure. On this line, take a point O nearly at the middle of it and draw a line OA such that ∠MOA is less than 90°. Then draw a normal ON on line MM1 at the point O, and place a small plane mirror vertical by means of a stand with its silvered surface along MM1 .

Next fix two pins P and Q at some distance (≈ 5 cm) apart vertically on line OA, on the board. Keeping eye on the other side of normal (but on the same side of mirror), see clearly images P' and Q' of the pins P and Q. Next fix a pin R such that it is in line with the images of pins P and Q as observed in the mirror. Next, fix one more pin S such that the pin S is in line with the pin R as well as images P' and Q' of pins P and Q.
Draw small circles on paper around the positions of pins as shown in figure. Remove the pins and draw a line OB joining the pin points S and R, which meets the surface of mirror at O. The angles AON and BON are measured and recorded.
The experiment is then repeated for the angle of incidence ∠AON equal to 40°, 50°, 60°.  From results, it is observed that angle of incidence is equal to the angle of reflection. This verifies the first law of reflection.
The experiment has been performed on a flat drawing board, with mirror normal to the plane of board on which white sheet of paper is being fixed. Since the lower tips of all the pins also lie on the same plane(i.e., the plane of paper), it proves the second law of reflection.

8. A light ray is incident normally on a plane mirror. (a) What is its angle of incidence?

(b) What is the direction of reflected ray? Show it on a diagram.

(a) 0o

(b) Same as the incident ray

9. Draw a diagram to show the reflection of a ray of light using a plane mirror. In the diagram, label the incident ray, the reflected ray, the normal, the angle of incidence and the angle of reflection.

10. Fig. 7.15 shows an incident ray AO and the normal ON on a plane mirror. The angle which the incident ray AO makes with mirror is 30. (a) Find the angle of incidence. (b) Draw the reflected ray and then find the angle between the incident and reflected rays. (a) Angle of incidence = 90– 30o = 60o

(b) Angle between the incident ray and reflected ray = Angle of incidence + Angle of reflection

Angle of reflection = Angle of incidence = 60o

Therefore, Angle between the incident ray and reflected ray = 60o + 60o = 120o

11. The diagram in Fig. 7.16 shows a point object in front of a plane mirror MM1.

(a) Complete the diagram by taking two rays from the point to show the formation of its image.

(b) In the diagram, mark the position of eye to see the image.

(c) Is the image formed real or virtual? Explain why?

(a) and (b)

(c) The image formed is virtual because the reflected rays meet when produced backwards.

12. The diagram below in Fig7.17. shows an object XY in front of a plane mirror. Draw on the diagram, the image of the object formed by the mirror. Trace the path of two rays from a point on the object to show the formation of image.

13. (a) Write three characteristics of the image formed by a plane mirror?

(b) How is the position of an image related to the position of the object?

(a) Three characteristics of image formed by plane mirror:

• Image formed in erect (upright)
• Image formed is virtual
• Image formed is of the same size as the object

(b) The image is situated at the same perpendicular distance behind the mirror as the object in front of it.

14. Differentiate between a real and a virtual image.

 Real Image Virtual image 1. A real image is formed due to actual intersection of the reflected rays. 1. A virtual image is formed when the reflected rays meet if they are produced backwards. 2. A real image can be obtained on a screen. 2. A virtual image cannot be obtained on a screen. 3. A real image is inverted with respect to the object. 3. A virtual image is erect with respect to the object.

15. What is meant by lateral inversion of an image in a plane mirror? Explain it with the help of a ray diagram.

The interchange of the left and right sides in the image of an object in a plane mirror is called lateral inversion.

Figure above shows the image formation of a letter P in a plane mirror. The letter P appears in the plane mirror as .

16. The letters on the front of an ambulance are written laterally inverted like . Give reason.

The letters on the front of a ambulance are written laterally inverted, so that the driver of the vehicle moving ahead of the ambulance reads these words laterally inverted as AMBULANCE, in his rear view mirror, and gives side to pass the ambulance first.

17. Why is it difficult to read the image of the text of a page formed due to reflection by a plane mirror?

Due to lateral inversion, , it becomes difficult to read the image of the text of a page formed due to reflection by a plane mirror.

### Multiple Choice Questions -7(A)

1. According to the law of reflection:

(a) i/r = constant

(b) sin i /sin r = constant

(c) i + r = constant

(d) i = r

(d) i = r

2. The image formed by a plane mirror has the following characteristic:

(a) Erect and diminished

(b) Erect and enlarged

(c) Inverted and of same size

(d) Erect and of same size.

(d) Erect and of same size

3. The image formed by a plane mirror is :

(a) real

(b) virtual

(c) virtual with lateral inversion

(d) real with lateral inversion

(c) virtual with lateral inversion

### Numerical -7(A)

1. The ray is incident on a plane mirror. Its reflected ray is perpendicular to the incident ray. Find the angle of incidence.

Angle of incidence (i) + Angle of reflection(r) = 90

But, as per the laws of reflection, i = r

Therefore, 2 i = 90o

Or, i = r = 45o

2. A man standing in front of a plane mirror finds his image at a distance 6 metre from himself. What is the distance of man from the mirror?

Distance between man and his image = 6m

Distance between man and mirror + distance between mirror and image = 6m

But, Distance between man and mirror (object distance) = distance between mirror and image (image distance)

Therefore, distance of man from mirror = 6/2 = 3m

3. An insect is sitting in front of a plane mirror at a distance 1 m from it.

(a) Where is the image of the insect formed?

(b) What is the distance between the insect and its image?

(a) Image of the insect is formed 1m behind the mirror.

(b) Distance between the insect and his image = 1 + 1 = 2 m

4. An object is kept at 60 cm in front of a plane mirror. If the mirror is now moved 25 cm away from the object, how does the image shift from its previous position?

Initially, distance of the object from the mirror = 60 cm.

Therefore, image is formed at a distance 60 cm from the mirror, behind it.

Thus, initial distance between the object and image = 60 + 60 = 120 cm

If the mirror is moved 25 cm away from the object,

The new distance of the object from the mirror = 60 + 25 = 85 cm

The new image is now at a distance 85 cm from the mirror behind it.

Thus, new distance of the image from the object = 85 + 85 = 170 cm

Taking the position of the object as reference point, the distance between the two positions of the image

= new distance of image from the object – initial distance of the image from the object

= (170 – 120) cm = 50 cm

Thus, the image shifts 50 cm away.

5. An optician while testing the eyes of a patient keeps a chart of letters 3 m behind the patient and asks him to see the letters on the image of chart formed in a plane mirror kept at distance 2 m in front of him. How far away is the chart seen by the patient?

Distance between man and chart = 3m

Distance between man and mirror = 2m

Therefore, distance between chart and mirror = 5 m

Now, final image is formed on the mirror, which is at a distance of 2 m from the man, therefore, the chart as seen by patient is (5m + 2m) = 7m away.

### Exercise -7(B)

1. Two plane mirrors are placed making an angle in between them. Write an expression for the number of images formed of an object placed in between the mirrors. State the condition, if any.

If two mirrors make an angle with each other and object is placed in between the two mirrors, the number of images formed is n or (n – 1) depending upon n = 360°/θ° is odd or even.

(a) If n = 360°/θ° is odd,

• The number of images formed is n, when the object is placed asymmetrically between the mirrors.
• The number of images formed is n-1, when the object is placed symmetrically between the mirrors.

(b) If n = 360oo is even, the number of images is always n-1.

2. Two plane mirrors are placed making an angle θ° in between them. For an object placed in between the mirrors, if angle is gradually increased from 0 to 180, how will the number of images change: increase, decrease or remain unchanged?

The number of images formed is given as, n = 360°/θ°

So, if θ is gradually increased, n decreases.

3. How many images are formed for a point object kept in between two plane mirrors M1and M2at right angles to each other? Show them by drawing a ray diagram.

For two mirrors kept perpendicular to each other, three images are formed for an object kept in between them.

4. Two plane mirrors are arranged parallel and facing each other at some separation. How many images are formed for a point object kept in between them? Show the formation of images with the help of a ray diagram

For two mirrors kept parallel to each other, an infinite number of images are formed for an object kept in between them.

5. State two uses of a plane mirror.

Two uses of plane mirror:

1. In barber’s shop for seeing the hairs at the back of head, two mirrors facing each other are fixed on opposite walls at the front and back of the viewer.
2. In solar heating devices such as a solar cooker, solar water heater, etc., a plane mirror is used to reflect the incident light rays from sun on the substance to be heated.

### Multiple Choice Questions -7(B)

1. Two plane mirrors are placed making an angle 60in between them. For an object placed in between the mirrors, the number of images formed will be :

(a) 3

(b) 6

(c) 5

(d) infinite.

(c) 5

2. In the barber’s shop, two plane mirrors are placed:

(a) Perpendicular to earth other

(b) Parallel to each other

(c) At an angle 60° between them

(d) At angle 45° between them

(b) In a barber’s shop, two plane mirrors are placed parallel to each other.

### Numerical -7(B)

1. State the number of images of an object placed between two mirrors, formed in each case when mirrors are inclined to each other at

(a) 90°, and

(b) 60°.

(a) Angle between the mirrors, = 90o

Now, n = 360°/θ° = 360o/90= 4, which is even.

Hence, number of images formed will be (n-1); i.e., 4-1 = 3 images

(b) Angle between the mirrors, = 60o

Now, n = 360o/θ° = 360o/60= 6, which is even.

Hence, number of images formed will be (n-1); i.e., 6-1 = 5 images

2. An object is placed (i) asymmetrically (ii) symmetrically, between two plane mirrors inclined at an angle of 50. Find the number of images formed.

Angle between the mirrors, = 50o

Now, n = 360°/θ° = 360o/50= 7.2 7, which is odd.

(i) When placed asymmetrically, number of images formed will be n, i.e. 7.

(ii) When placed symmetrically, number of images formed will be (n-1); i.e. 7-1 = 6 images

### Exercise -7(C)

1. What is a spherical mirror?

A reflecting surface which is a part of a sphere is called a spherical mirror.

2. Name the two kinds of spherical mirrors and distinguish between them.

Two kinds of spherical mirrors are concave and convex.

Distinction between concave and convex mirror: A concave mirror’s bulging surface is silvered and reflection takes place from the hollow surface but a convex mirror’s inner surface is silvered and reflection takes place from the bulging surface.

3. Define the terms pole, principal axis and centre of curvature with reference to a spherical mirror.

Pole: The geometric centre of the spherical surface of mirror is called the pole of mirror.

Principal axis: It is the straight line joining the pole of the mirror to its centre of curvature.

Centre of curvature: The centre of curvature of a mirror is the centre of the sphere of which the mirror is a part.

4. Draw suitable diagrams to illustrate the action of (i) concave mirror and (ii) convex mirror on a beam of light incident parallel to the principal axis.

5. Name the spherical mirror which (i) diverges (ii) converges the beam of light incident on it. Justify your answer by drawing a ray diagram in each case.

(i) Convex mirror diverges a beam of light falling on it.

6. Define the terms focus and focal length of a concave mirror. Draw diagram to illustrate your answer.

Focus of a concave mirror: The focus of a concave mirror is a point on the principal axis through which the light rays incident parallel to principal axis, pass after reflection from the mirror.

Focal length of a concave mirror: The distance of the focus from the pole of the concave mirror is called its focal length.

7. Explain the meaning of the terms focus and focal length in case of a convex mirror, with the help of suitable ray diagram.

Focus of a convex mirror: The focus of a convex mirror is a point on the principal axis from which, the light rays incident parallel to principal axis, appear to come, after reflection from the mirror.

Focal length of a convex mirror: The distance of the focus from the pole of the convex mirror is called its focal length.

8. State the direction of incident ray which after reflection from a spherical mirror retraces its path. Give a reason to your answer.

Incident ray is directed towards the centre of curvature because the ray is normal to the spherical mirror, So, i = r = O.

9. (i) Name the mirrors shown in Fig. 7.49 (a) and (b).

(ii) In each case (a) and (b), draw reflected rays for the given incident rays and mark focus by the symbol F.

(i) In figure (a) a convex mirror is shown.

In figure (b) a concave mirror is shown.

(ii) (a)

10. Complete the following diagrams in Fig.7.50 by drawing the reflected rays for the incident rays 1 and 2.

11. Complete the following diagrams shown in Fig. 7.51 by drawing the reflected ray for each of the incident ray A and B

12. State the two convenient rays that are chosen to construct the image by a spherical mirror for a given object? Explain your answer with the help of suitable ray diagrams.

Two convenient rays that are chosen to construct the image by a spherical mirror for a given object:

1. A ray passing through the centre of curvature: A ray of light passing through the centre of curvature of a concave mirror or a ray directed in the direction of centre of curvature of a convex mirror is reflected back along the same path after reflection.
1. A ray parallel to the principal axis: A ray of light parallel to the principal axis, after reflection pass through the principal focus in case of a concave mirror or appears to diverge from it in case of convex mirror.

13. Fig. 7.52 shows a concave mirror with its pole at P, focus and centre of curvature C. Draw ray diagram to show the formation of image of an object OA. 14. Fig. 7.53 shows a concave mirror with its pole at P, focus F and centre of curvature C. Draw ray diagram to show the formation of image of an object OA.

15. The diagram below in Fig.7.54, shows a convex mirror. C is its centre of curvature and F is its focus. (i) Draw two rays from A and hence locate the position of image of object OA. Label the image IB. (ii) State three characteristics of the image.

The ray diagram shows two light rays from A.

The image of the object OA is formed between the focus and the pole on the other side of the mirror.

The image so formed is erect, virtual and diminished.

16. Draw a ray diagram to show the formation of image by a concave mirror for an object placed between its pole and focus. State three characteristics of the image.

Ray diagram showing the formation of an image by a concave mirror for an object placed between its pole and focus:

When the object is placed between focus F and pole P, the image is formed behind the mirror.

The image so formed is virtual, upright and magnified.

17. Draw a ray diagram to show the formation of image by a concave mirror for the object beyond its centre of curvature. State three characteristics of the image.

Ray diagram showing the formation of an image by a concave mirror for the object beyond its centre of curvature:

When the object is placed beyond the centre of curvature C, the image is formed between focus F and centre of curvature C. The image so formed is real, inverted and diminished.

18. Draw a ray diagram to show the formation of image of an object kept in front of a convex mirror. State three characteristics of the image.

The image formed is virtual, erect and diminished.

19. Name the mirror which always produces an erect and virtual image. How is the size of image related to the size of object?

Convex mirror always produces erect and virtual images. The images formed are diminished, i.e. the size of the image is shorter than the size of the object.

20. (a) For what position of object, the image formed by a concave mirror is magnified and erect?

(b) State whether the image in part (a) is real or virtual?

(a) If the object is placed between the pole and focus of a concave mirror, the image formed is magnified and erect.

(b) The image is virtual.

21. (a) State the position of object for which the image formed by a concave mirror is of same size.

(b) Write two more characteristics of the image.

(a) If the object is placed at the centre of curvature of a concave mirror, the image formed is of same size.

(b) The image formed is real and inverted.

22. (a) What is a real image?

(b) What type of mirror can be used to obtain a real image of an object?

(c) Does the mirror mentioned in part (b) form real image for all locations of the object?

(a) An image which can be obtained on a screen is called a real image.

(b) A concave mirror can be used to obtain a real image of an object.

(c) No, it does not form real image for all locations of the object.

23. Discuss the position and nature of image formed by a concave mirror when an object is moved from infinity towards the pole of mirror.

When an object is moved from infinity towards the pole of mirror, the image formed moves away from the mirror. The image formed is real and inverted.

24. Discuss the position and nature of image formed by a convex mirror when an object is moved from infinity towards the pole of mirror.

In a convex mirror, the image formed is always virtual, upright and diminished. It is always situated between its pole and focus, irrespective of the distance of object in front of the mirror.

25. Name the kind of mirror used to obtain:

(a) A real and enlarged image,

(b) A virtual and enlarged image,

(c) A virtual and diminished image,

(d) A real and diminished image.

(a) Concave,

(b) Concave,

(c) Convex

(d) Concave

26. How is the focal length of a spherical mirror related to its radius of curvature?

Focal length is half the radius of curvature of a spherical mirror.

F = R/2

27. Write the spherical mirror’s formula and explain the meaning of each symbol used in it.

The spherical mirror’s formula is

1/u + 1/v = 1/f

Here, u is the object distance, v is the image distance and f is the focal length of the mirror.

28. What is meant by magnification? Write its expression. What is its sign for the (a) real (b) virtual, image?

Magnification is the ratio of the length of image to the length of the object.

m = i/o

It is also given as

m = -v/u

Where, u and v is the object and image distance, respectively.

Hence, we have

(a) For real image: u and v are negative. So, m is negative.

(b) For virtual image: u is negative and v is positive. So, m is positive.

29. At what maximum distance the image in a convex mirror can be obtained? What will be the location of object then?

The image formed by a convex mirror is always between pole and focus. Hence, the maximum distance that can be obtained in convex mirror is the focal length. For this case the object has to be at infinity.

30. Upto what maximum distance from a concave mirror, the image can be obtained? What will be the location of object for it?

The maximum distance that can be obtained in concave mirror is infinity. For this case the object has to be at focus.

31. How will you distinguish between a plane mirror, a concave mirror and a convex mirror, without touching them?

To distinguish between a plane mirror, concave mirror and convex mirror, the given mirror is held near the face and image is seen. There can be following three cases:

• Case (i): If the image is upright, of same size and it does not change in size by moving the mirror towards or away from the face, the mirror is plane.
• Case (ii): If the image is upright and magnified, and increases in size on moving the mirror away, the mirror is concave.
• Case (iii): If the image is upright and diminished and decreases in size on moving the mirror away, the mirror is convex.

32. State two uses of a concave mirror.

Two uses of concave mirror:

• It is used as a shaving mirror.
• It is used as reflector in torch, head light of automobiles etc.

33. State the kind of mirror used

(a) By a dentist,

(b) As a search-light reflector.

(a) Concave mirror

(b) Concave mirror

34. (a) When a concave mirror is used as a shaving mirror, where is the person’s face in relation to the focus of mirror?

(b) State three characteristics of the image seen in part (a).

(a) The person’s face is between the pole and focus of the mirror.

(b) The image formed is erect, virtual and magnified.

35. Which mirror will you prefer to use as a rear view mirror in a truck: plane mirror or convex mirror? Give one reason.

A convex mirror is preferred as a rear view mirror because it has a wider field of view as compared to a plane mirror of same size.

36. Why does a driver use a convex mirror as a rear view mirror? Illustrate your answer with the help of a ray diagram.

A convex mirror diverges the incident beam and always forms a virtual, small and erect image between its pole and focus. Thus, a driver can see all the traffic approaching from behind. This fact enables the driver to use it as a rear view in vehicles to see all the traffic approaching from behind.

### Multiple Choice Questions -7(C)

1. For an incident ray directed towards centre of curvature of a spherical mirror the reflected ray:

(a) Retraces its path

(b) Passes through the focus

(c) Passes through the pole

(d) Becomes parallel to the principal axis.

(a) Retraces its path

2. The image formed by a convex mirror is

(a) Erect and diminished.

(b) Erect and enlarged.

(c) Inverted and diminished.

(d) Inverted and enlarged.

(a) Erect and diminished

3. A real and enlarged image can be obtained by using a

(a) Convex mirror

(b) Plane mirror

(c) Concave mirror

(d) Either convex or plane mirror.

(c) Concave mirror

### Numerical -7(C)

1. The radius of curvature of a convex mirror is 40 cm. Find its focal length.

Focal length = ½ (Radius of curvature)

Or, f = 40/2 = 20 cm

2. The focal length of a concave mirror is 10 cm. Find its radius of curvature.

Radius of curvature = 2 focal length

Or, R = 2f = 2 10 = 20 cm

3. An object of height 2 cm is placed at a distance 20 cm in front of a concave mirror of focal length 12 cm. Find the position, size and nature of the image by drawing.

The image is 30 cm in front of the mirror, 3 cm high, real, inverted and magnified.

4. An object is placed at 4 cm distance in front of a concave mirror of radius of curvature 24 cm. Find the position of image by drawing. Is the image magnified?

The image is 6 cm behind the mirror.

Yes, the image is magnified.

5. At what distance from a concave mirror of focal length 25 cm should an object be placed so that the size of image is equal to the size of the object. Draw a ray diagram to show this.

The size of the image is equal to the size of the object if the object is placed at the centre of curvature of a concave mirror.

Hence, the object should be placed at 50 cm.

6. An object 5 cm high is placed at a distance 60 cm in front of a concave mirror of focal length 10 cm. Find the position and size of the image by drawing.

The position of the object is 12 cm in front of the mirror.

Its size is 1 cm.

7. A point light source is kept in front of a convex mirror at a distance of 40 cm. The focal length of the mirror is 40 cm. Find the position of image by drawing.

The image is behind the mirror at a distance 20 cm

8. When an object of height 1 cm is kept at a distance 4 cm from a concave mirror, its erect image of height 1.5 cm is formed at a distance 6 cm behind the mirror. Find the focal length of mirror, by drawing.

A ray passing parallel to the principal axis passes through the focal point after reflection. Hence, the focal length is 12 cm.

9. An object of length 4 cm is placed in front of a concave mirror at distance 30 cm. The focal length of mirror is 15 cm.

(a) Where will the image form?

(b) What will be the length of image?

O = 4 cm
u = - 30 cm
f = - 15 cm
From mirror formula ,

10. A concave mirror forms a real image of an object placed in front of it at a distance 30 cm, of size three times the size of object. Find (a) the focal length of mirror (b) position of image.

u = - 30 cm

11. A concave mirror forms a virtual image of size twice that of the object placed at a distance 5 cm from it.

Find : (a) the focal length of the mirror (b) position of image

m = I/O = 20/O = 2
∵ m = -v/u
∴ -v/u = 2
∴ - v = 2u
∵ u = -5 cm
∴ v = 10 cm
Hence, the position of the image is 10 cm behind the mirror.
From mirror formula,

12. The image formed by a convex mirror is of size one third the size of object. How are u and v related?

13 . The erect image formed by a concave mirror is of size double the size of object. How are u and v related?

Magnification is
m = I/O = 20/O = 2
∵ m = -v/u
∴ -v/u = 2
∴ v = -2u
But, u is always negative
∴ v = 2u

14. The magnification for a mirror is -3. How are u and v related?

Magnification of a mirror is

m = -v/u

⇒ m = -3

⇒ -3 = -v/u

⇒ v = 3u

But, u will always be negative

∴ v = -3u