Lakhmir Singh Class 10 Physics 4th Chapter Reflection of Light Solution

Lakhmir Singh Manjit Kaur Physics Solution:- Reflection of Light Chapter 4. Here you get easy Solutions of Lakhmir Singh Class 10 Physics Solution Chapter 4. Here we have given Chapter 4 all Solution of Class 10. Its help you to complete your homework.

Board – CBSE
Text Book – Physics
Class – 10
Chapter – 04

Lakhmir Singh Class 10 Physics 4th Chapter Solution

1.) What happens when a ray of light falls normally (or perpendicularly) on the surface of a plane mirror?
Ans:
When a ray of light falls normally or perpendicularly on the surface of a plane mirror then angle of incidence for such mirror is zero which means that angle of reflection also zero. And hence the ray of light incident normally on the plane mirror get reflected back along the same path.

2.) A ray of light is incident on a plane mirror at an angle of 30°. What is the angle of reflection?
Ans:
If a ray of light is incident on a plane mirror at an angle of 30° then the angle of reflection will be 30°.

3.) A ray of light strikes a plane mirror at an angle of 40° to the mirror surface. What will be the angle of reflection?
Ans:
If a ray of light strikes a plane mirror at an angle of 40° to the mirror surface,then the angle of reflection will be 50°.

4.) A ray of light is incident normally on a plane mirror. What will be the:
(a) angle of incidence?
(b) angle of reflection?
Ans:
If a ray of light is incident normally on a plane mirror, then
a)) Angle of incidence is zero.
b) And angle of reflection is also zero.

5. What type of image is formed:
(a) in a plane mirror?
(b) on a cinema screen?

Ans:

a) the image formed in a plane mirror is the virtual image.

b) the image formed on a cinema screen it the real image.

6.) What kind of mirror is required for obtaining a virtual image of the same size as the object?

Ans:

Plane mirror is required for obtaining a virtual image of the same size as the object.

7.) What is the name of the phenomenon in which the right side of an object appears to be the left side of the image in a plane mirror?

Ans:

The phenomenon in which the right side of an object appears to be the left side of the image in a plane mirror is called as lateral inversion.

8.) Name the phenomenon responsible for the following effect: When we sit in front of a plane mirror and write with our right hand, it appears in the mirror that we are writing with the left hand.

Ans:

When we sit in front of a plane mirror and write with our right hand it appears in the mirror that we are writing with the left hand such a phenomenon is called as lateral inversion.

9.) If an object is placed at a distance of 10 cm in from of a plane mirror, how far would it be from its image?

Ans:

As the object is placed at a distance of 10cm in front of mirror that means the image will be formed at a distance of 10cm behind the mirror from the mirror. So total distance of image from the object will be 10+10= 20cm.

10.) Which property of light makes a pencil cast a shadow when it is held in front of a light source?

Ans:

The rectilinear propagation of light i.e., light always travels in straight line makes a pencil cast a shadow when it is held in front of a light source.

11.) The image seen in a plane mirror cannot be formed on a screen. What name is given to this type of image?

Ans:

If the images seen in a plane mirror cannot be formed on a screen, then this type of image is called as virtual image.

12.) Fill in the following blank with a suitable word:

Ans:

When light is reflected the angles of incidence and reflection are equal.

13.) State whether the following statement is true or false: A student says that we can see an object because light from our eyes is reflected back by the object.

Ans:

The above statement is false. Because we can see the objects with our eyes due to reflection of light from the object which is scattered and diffused also.

14.) Where is the image when you look at something in a mirror?
Ans:
When we look at something in a mirror then image will be formed behind the mirror.

15.) A ray of light strikes a plane mirror such that its angle of incidence is 30°. What angle does the reflected ray make with the mirror surface?
Ans:
If a ray of light strikes a plane mirror such that it’s angle of incidence is 30° then the angle made by reflected ray with the mirror surface will be 60°.

Short Answer Type Questions

16. What is the difference between a real image and a virtual image? Give one example of each type of image.
Ans:
The image which can be obtained on the screen such image is called as the real image.

For example:

All the images formed on screen in cinema halls are the real images as they are obtained on the screen.
The image which cannot be obtained on a screen is called as the virtual image.

For example:

The image formed in plane mirror of any object is the virtual image.

17. The letter F is placed in front of a plane mirror:
(a) How would its image look like when seen in a plane mirror?
(b) What is the name of the phenomenon involved?

Ans:

a) If a letter F is placed in front of plane mirror, then it’s image look likes laterally inverted as shown below.

b) The phenomenon involved here is called as lateral inversion.

18.) What is lateral inversion? Explain by giving a suitable example.

Ans:

When any object placed in front of plane mirror then we observed that right side of object appears as left side of the image. And in the same way left side of object appears as right side of the image. This change in sides of the object and it’s image in plane mirror is called as lateral inversion.
That means the image formed in a plane mirror is laterally inverted with respect to the object.

For example:-

If we are sitting in front of plane mirror then we observed that the image formed in mirror is somewhat laterally inverted which means our left hand in image will become right hand and our right hand will become left hand in image formed.
And this is called as lateral inversion which is due to reflection of light.
Also when we see the image of word RED in mirror it look somewhat like as shown in figure and this phenomenon is called as lateral inversion.

19.) Write the word AMBULANCE as it would appear when reflected in a plane mirror. Why is it sometimes written in this way (as its mirror image) on the front of an ambulance?

Ans:

The word AMBULANCE appears when reflected in a plane mirror as given below in the figure.

The word AMBULANCE is written on the hospital vans in the form of its mirror image (Because when we are driving vehicles and if the ambulance van is coming from behind our vehicle and we saw it in our rear-view mirror then we see the laterally inverted image and read it as AMBULANCE)
Because, ambulance is working for carrying serious patients who need diagnosis earlier so to avoid traffic and to make path for traveling through traffic on the hospital vans the name ambulance is written in lateral inversion form and hence we can see it’s image correctly and we can make way for it so that the patient will go fast to the hospital to recover early.

20) What are the important differences between looking at a photograph of your face and looking at yourself in a plane mirror?

Ans:-

The image formed in photograph is the real image taken on a photographic plate and whose printed copy we are seeing.
The image in photograph is the real image and which is small in size as compared to the object.
While when we see our face in plane mirror we see virtual image of us which cannot taken on photographic film.
And the virtual image formed in plane mirror is having same size as compared to the size of the object.

21)

(a) A wall reflects light and a mirror also reflects light) What difference is there in the way they reflect light?

(b) Which type of reflection of light leads to the formation of images?

Ans:

When light rays are incident on the wall which is a rough surface due to which light get reflected in all directions Whereas when light is incident on the mirror which is a plane or smooth surface then light get reflected in only one direction.
This is the main difference between the reflection of light from wall and the plane mirror.

b)
As the reflection from mirrors which is smooth surface gives rise to regular reflection of light rays and hence it leads to formation of image.

22) What is the difference between regular reflection of light and diffuse reflection of light? What type of reflection of light takes place from?

(a) a cinema screens

(b) a plane mirrors

(c) a cardboard

(d) still water surface of a lake

Ans:

Regular reflection of light:

If we incident a parallel beam of light then it will be reflected as parallel beam in only one direction in regular reflection of light as shown in figure below.
Regular reflection occurs only when light beam is incident on smooth surfaces or highly polished metal surfaces.
For example: reflection of light from a plane mirror is the regular reflection of light

Diffused reflection of light:

In diffused reflection of light if we incident parallel beam of light then it will be reflected in different directions as shown in figure below.
Diffused reflection of light occurs only when parallel beam of light is incident on rough surfaces like paper, cardboard, chalk, table, chair, walls and unpolished metal objects.

a) Diffused type of reflection of light takes place from a cinema screen.
b) Regular type of reflection of light takes place from plane mirrors.
c) Diffused type of reflection of light takes place from a cardboard)
d) Regular type of reflection of light takes place from the still lake of water.

23) What can you see in a completely dark room? If you switch on an electric bulb in this dark room as a light source, explain how you could now see:

(a) the electric bulb)

(b) a piece of white paper)

Ans:

As the room is completely dark, we can’t see anything because there is no light to see.

a)
When we switch on an electric bulb in dark room then we see only that bulb and nothing else because the light from the bulb goes into our eyes and hence, we can see that bulb only.

b)
If in a dark room electric bulb is glowing and some white paper is placed also then we can see that white paper also because the light emitted from electric bulb reaches to that paper and undergoes diffused light reflection due to which we can see it.

24) (a) A boy with a mouth 5 cm wide stands 2 m away from a plane mirror) Where is his image and how wide is the image of his mouth?

(b) The boy walks towards the mirror at a speed of 1 m/s) At what speed does his image approach him?

Ans:

Since given that, boy is having mouth of 5cm in wide and he stands 2 m away from a plane mirror.
As we know that, in case of plane mirror the image formed will be at a same distance behind the plane mirror and whose size is same as that of the object size.
Hence, here the image will be formed 2m behind the plane mirror and the size of the image would be 5cm.

Since, the boy is walking towards the mirror with a speed of 1m/s and hence the speed of image approaching him will be 2m/s) Because it is the sum of speed of image moving towards the mirror and also the speed of boy) Hence, speed of image (1+1) = 2m/s.

25) (a) An extended object in the form of an arrow pointing upward has been placed in front of a plane mirror) Draw a labelled ray-diagram to show the formation of its image) (b) State the uses of plane mirrors.

Ans:

a)
The following figure shows the image formed of an extended object in the form of an arrow pointing upward has been placed in front of the plane mirror.

Following are the uses of plane mirrors:

Plane mirrors are mostly used to see images of ourselves. Such as mirrors in our dressing table and in bathrooms.
In certain shops like jewellery shops plane mirrors are fixed from inside to see the look bigger.
In making periscopes plane mirrors are also used.

Long Answer Type Questions

26) What is meant by ‘reflection of light’? Define the following terms used in the study of reflection of light by drawing a labelled ray-diagram:

(a) Incident ray

(b) Point of incidence

(c) Normal

(d) Reflected ray

(e) Angle of incidence

(f) Angle of reflection

Ans:

When a ray of light is incident on the object then it will be sent back in the same medium which is called as reflection of light.

The following diagram shows the reflection of light.

Incident ray is the ray which is incident on the surface of mirror.
In figure AO is the incident ray.

Point of incidence is that point at which the incident ray meets the surface of mirror.
In figure O is the point of incidence.

The line drawn at the point of incidence which is perpendicular to the surface of mirror is called as normal.
The line MN shows the normal in figure.

The incident ray after striking the surface of mirror get send back into the same medium which is called as reflected ray.
In figure OB is the reflected ray.

Angle of incidence is that angle which is made by incident ray with the normal at the point of incidence.
The angle AOM is the angle of incidence and it is denoted by i.

Angle of reflection is that angle which is made by reflected ray with the normal at the point of incidence.
The angle BOM is the angle of reflection and it is denoted by r.

27.) State and explain the laws of reflection of light at a plane surface (like a plane mirror), with the help of a labelled ray-diagram. Mark the angles of ‘incidence’ and ‘reflection’ clearly on the diagram. If the angle of reflection is 47.5°, what will be the angle of incidence?

Ans:

Laws of reflection:-

The laws of reflection of light when light is reflected from plane surface such as plane mirror are given as below.

1) According to first law of reflection of light, the incident ray, reflected ray and the normal at the point of incidence all lies in the same plane as shown in figure below.
From figure, incident ray AO, reflected ray OB and the normal MN at the point of incidence O all lie in the same plane.

2) According to second law of reflection of light, the angle of reflection and angle of incidence are always equal as shown in figure below.
From figure, the angle of incidence AON and the angle of reflection BON both are equal.

Hence, <i = <r

If the angle of reflection is 47.5° then the angle of incidence will be 47.5°. since according to second law of reflection of light.

28.) With the help of a labelled ray-diagram, describe how a plane mirror forms an image of a point source of light placed in front of it. State the characteristics of the image formed in a plane mirror.

Ans:

Formation of image by plane mirror:

The following figure shows the how plane mirror forms an image of a point source of light placed in front of it.
Let us consider a point object O is placed in front of the plane mirror MM’ as shown in figure.
The object O which gives light rays in all directions but the ray of light OA which is coming from the object O is incident on the plane mirror at point A. And this incident ray OA get reflected according to laws of reflection in the direction AX.
Let us suppose for the incident ray OA and reflected ray AX the angle of incidence is i1 and angle of reflection is r1.

Now, the second ray OB is coming from the source object O, which strikes the mirror at point B and after reflection goes in the direction BY as shown in figure.
For this ray we consider angle of incidence as i2 and angle of reflection as r2.
We observed that the rays AX and BY are diverging and they can’t meet on the left side.
We extend the rays AX and BY in backward direction as a dotted line as shown in figure. We see that, the extended rays AX and BY meets at point I behind the mirror. When this rays AX and BY enters to our eyes E then we see that some source I is placed behind the mirror from which we are seeing light rays in straight line.
And hence point I behind the mirror is the image of the object O which is formed in plane mirror.
So, if our face is at point O then we see the image of our face at point I behind the mirror.

Following are the characteristics of the image formed by the plane mirror:

The image of the object formed in plane mirror is the virtual image and it cannot take on the screen.
Also, the image formed in the plane mirror is erect and its size is same as the object size.
The distance of the image from the mirror is same as the distance of the object from the mirror.
And most importantly, the image formed in plane mirror is laterally inverted.

29.) (a) Explain why, though both a plane mirror and a sheet of paper reflect light but we can see the image of our face in a plane mirror but not in a sheet of paper.

(b) The image in a plane mirror is virtual and laterally inverted. What does this statement mean?

(c) Write all the capital letters of the alphabet which look the same in a plane mirror.

Ans:

Although both a plane mirror and a sheet of paper reflects light but we can see the image of our face in a plane mirror but not in a sheet of paper.
Because, plane mirror is having smooth surface and when parallel beam of light is incident on the plane mirror it gets reflected only in one direction as parallel beam.
And this is called as regular reflection of light in which light rays after reflection meets at a point behind the plane mirror where is the image will be formed.
So, we can see our image in plane mirror due to regular reflection of light.
But, when a parallel beam of light is incident on the sheet of paper which is rough surface then after reflection the parallel beam of light get reflected in all directions which is called as discussed reflection of light.
And hence this ray after reflection does not meet at any point and hence no image will be formed.
Thus, we cannot see image of our face in sheet of paper but we can see image in plane mirror.

The image in a plane mirror is virtual and laterally inverted it means that the image formed in plane mirror is the virtual image which is formed behind the mirror and hence it cannot be taken on the screen.
Also, the left side of object appears right side in image and right side of the object appears left side in the image formed in a plane mirror.
And all this phenomenon is called as lateral inversion.

Following are the capital letters of alphabet which looks same in the plane mirror:
A, H, M, O, I, T, W, X and V.

Spherical Mirrors

Very Short Answer Type Questions

1) Name the spherical mirror which has:

(a) virtual principal focus.

(b) real principal focus.

Ans:

a)Convex mirror has virtual principal focus.

b)Concave mirror has real principal focus.

2.) Out of convex mirror and concave mirror, whose focus is situated behind the mirror?

Ans:

Out of convex and concave mirror the focus of convex mirror is situated behind the mirror.

3.) Find the focal length of a concave mirror whose radius of curvature is 32 cm.

Ans:

We know that, the relationship between focal length f and radius of curvature of concave mirror as,
R= 2f
Thus, f= R/2= 32/2 = 16cm
Thus, the focal length of a concave mirror would be 16cm.

4.) If the focal length of a convex mirror is 25 cm, what is its radius of curvature?

Ans:

We know that, the relationship between focal length f and radius of curvature R of the mirror is
R= 2f = 2*25= 50cm.
Thus, the focal length of convex mirror is 50cm.

5.) Fill in the following blanks with suitable words:

Ans:

a) Parallel rays of light are reflected by a concave mirror to a point called the principal focus.

b)The focal length of a concave mirror is the distance from the principal focus to the mirror.

c)A concave mirror converges rays of light whereas a convex mirror diverges rays of light.

d)For a convex mirror, parallel rays of light appear to diverge from a point called principal focus.

Short Answer Type Questions

6.) What is a spherical mirror? Distinguish between a concave mirror and a convex mirror.

Ans:

Spherical mirrors are those mirrors whose reflecting surface is the part of the hollow sphere.
There are two types of spherical mirrors that are concave mirrors and convex mirrors.

Concave mirror:

Concave mirror is the spherical mirror in which reflection of light takes place at the concave surface of the mirror.
The focus of the concave mirror is real and it is in front of the mirror.
Concave mirror is also called as converging mirror as it converges all the ray’s incident on it.
The image formed by the concave mirror is real or virtual.

Convex mirror:

Convex mirror is the spherical mirror in which reflection of light takes place from convex surface of the mirror.
The focus of the convex mirror is virtual and it is situated behind the mirror.
Convex mirror is also called as diverging mirror as it diverges all the ray’s incident on it.
The image formed by the convex mirror is always virtual.

7.) Name the two types of spherical mirrors. What type of mirror is represented by the?

(a) back side of a shining steel spoon?

(b) front side of a shining steel spoon?

Ans:

There are two types of spherical mirrors namely concave mirror and convex mirrors.

a)The back side of a shining steel spoon is the convex type of spherical mirror.

b)The front side of a shining steel spoon is the concave type of spherical mirror.

8.) What is the relation between the focal length and radius of curvature of a spherical mirror (concave mirror or convex mirror)? Calculate the focal length of a spherical mirror whose radius of curvature is 25 cm.

Ans:

The relation between the focal length f and the radius of curvature R of a spherical mirror is given by,

R= 2f
Given that, R= 25cm.
Hence, f= R/2= 25/2= 12.5 cm

Thus, the focal length of the spherical mirror will be 12.5 cm

9.) Explain with a suitable diagram, how a concave mirror converges a parallel beam of light rays. Mark clearly the pole, focus and centre of curvature of concave mirror in this diagram.

Ans:

The following diagram shows the, how a concave mirror converges a parallel beam of light rays’ incident on it.

10) Describe with a suitable diagram, how a convex mirror diverges a parallel beam of light rays. Mark clearly the pole, focus and centre of curvature of convex mirror in this diagram.

Ans:

The following diagram shows the, how a convex mirror diverges a parallel beam of light rays’ incident in it.

Long Answer type Questions

11.) Define

(a) centre of curvature

(b) radius of curvature

(c) pole

(d) principal axis, and

(e) aperture, of a spherical mirror with the help of a labelled diagram.

Ans:

a) Centre of Curvature:

The spherical reflecting surface has its own centre i.e., centre of sphere which is called as centre of curvature of spherical mirror.
It is denoted by C.
In case of concave mirror, it lies towards the reflecting surface.

b) Radius of Curvature:

Radius of curvature is the radius of spherical reflecting surface forming the spherical mirror.
It is denoted by R.

c) Pole:

Pole of the spherical mirror is the centre point on the reflecting surface of spherical mirror.
It is denoted by P.

d) Principal Axis:

The line joining the distance between the pole and the centre of curvature of spherical mirror is called as principal axis of spherical mirror.
Principal axis is always perpendicular to the spherical mirror at its pole.

e) Aperture:

The diameter of the reflecting surface of spherical mirror is called as aperture of spherical mirror.

12. (a) Define

(i) principal focus of a concave mirror, and

(ii) focal length of a concave mirror.

(b) Draw diagram to represent the action of a concave mirror on a beam of parallel light rays. Mark on this diagram principal axis, focus F, centre of curvature C, pole P and focal length f, of the concave mirror.

Ans:

a) Principal focus of a concave mirror:

Consider the parallel beam of light is incident on the reflecting surface of a concave mirror as shown in figure below.
After reflecting from the concave surface, all these rays meet at a same point on the principal axis.
The point at which all the rays meet on the principal axis is called as principal focus or focal point of the concave mirror.
The principal focus or focal point is represented by F.

Focal length of concave mirror:

The distance between the principal focus and the pole of the mirror is called as the focal length of the concave mirror.
It is denoted by f.

Consider the parallel beam of light is incident on the reflecting surface of a concave mirror as shown in figure above.
After reflecting from the concave surface, all these rays meet at a same point on the principal axis. The point at which all the rays meet on the principal axis is called as principal focus or focal point of the concave mirror.

13)

(a) What is meant by

(i) principal focus of a convex mirror, and

(ii) focal length of a convex mirror?

(b) Draw diagram to show the action of convex mirror on a beam of parallel light rays. Mark on this diagram principal axis, focus F, centre of curvature C, pole P and focal length f, of the convex mirror.

Ans:

a) Principal focus of the convex mirror:-

In case of convex mirror, the reflected rays coming from reflecting surface of convex mirror are appears to come from a common point behind the reflecting surface on principal axis as shown in figure below.
This common point on principal axis is called as principal focus or focal point of the convex mirror.
The principal focus or focal point is represented by F.

Focal length of the convex mirror:

The distance between the principal focus and the pole of the mirror is called as the focal length of convex mirror.
It is denoted by f.

Rules for images formed by Concave Mirrors

Very Short Answer Type Questions

1) For what position of an object, a concave mirror forms a real image equal in size to the object?

Ans:

When the object is placed at the centre of curvature C of the concave mirror then the image formed will be at the centre of curvature C which is real and inverted and of the same size as that of the object as shown in figure below.

2) Where should an object be placed in front of the concave mirror so as to obtain its virtual, erect and magnified image?

Ans:

When an object is placed between pole P and focus F of a concave mirror then the image formed will be behind the mirror which is virtual, erect and also magnified as shown in figure below.

3) For which positions of the object does a concave mirror produce an inverted, magnified and real image?

Ans:

When the object is placed at the focus F of a concave mirror then the image formed will be at infinity which is real, inverted and highly magnified as shown in figure below.

4) If an object is placed at the focus of a concave mirror, where is the image formed?

Ans:

If the object is placed at the focus F of concave mirror, then image will be formed at infinity as shown in fig.

5) If an object is at infinity (very large distance) in front of a concave mirror, where is the image formed?

Ans:

When the object is at infinity from a concave mirror then image will be formed at the focus F which is real, inverted, point size and highly diminished as shown in figure below.

6) For what position of an object, a real and diminished image is formed by a concave mirror?

Ans:

When the object is at infinity from a concave mirror then image will be formed at the focus F which is real, inverted, point size and highly diminished as shown in figure below.

7) Copy this figure in your answer book and show the direction of the light ray after reflection:

Ans:

The ray of light passing through focal point will be reflected parallel to principal axis in case of concave mirror as in figure below.

8) Draw the following diagram in your answer book and show the formation of image of the object AB with the help of suitable rays:

Ans:

9) Draw the following diagram in your answer book and show the formation of image with the help of suitable rays:

Ans:

10) Which type of mirror could be used as a dentist’s mirror?

Ans: Concave mirrors are used by dentist to see the large image of teeth of patients.

Short Answer Type Questions

11) Which kind of mirror is used in the headlights of a car? Why is it used for this purpose?

Ans: Concave mirrors are used in the headlights of a car. Because when we place lighted bulb at the focus of concave reflector then there will be powerful parallel beam of light rays is produced. Due to which we can see the things up to a certain distance in dark also.

12) Explain why, a ray of light passing through the centre of curvature of a concave mirror gets reflected back along the same path.

Ans:

As shown in figure, we know that when a ray of light passes through the centre of curvature of a concave mirror it is reflected along the same path.

Here the ray of light AB is passing through the centre of curvature C of the concave mirror and it falls normally on the mirror at point B and it reflects back along the same path as ray BA.
The arrow pointing from left to right is the incident ray and the ray pointing from right to left is the reflected ray.
The ray passing through the centre of curvature C of concave mirror reflects back along the same path because it strikes the mirror at angle of 90° and hence angle of incidence and angle of reflection both are zero.

13.) What is the minimum number of rays required for locating the image formed by a concave mirror for an object? Draw a ray diagram to show the formation of a virtual image by a concave mirror.

Ans:

The minimum number of rays required for locating the image formed by a concave mirror for an object are two rays.
When the object is placed between pole P and focus F of concave mirror then the image is formed behind the mirror which is virtual, erect and magnified as shown in figure.

14) With the help of a ray diagram, determine the position, nature and size of the image formed of an object placed at the centre of curvature of a concave mirror.

Ans:

When the object is placed at the centre of curvature of the concave mirror then the image will be formed at the centre of curvature which is real, inverted and of the same size as the object as shown in following ray diagram.

15) Describe with the help of a diagram, the nature, size and position of the image formed when an object is placed beyond the centre of curvature of a concave mirror.

Ans:

When the object is placed behind the centre of curvature of concave mirror then the image will be formed between focus F and centre of curvature C which is real, inverted and diminished as shown in the following ray diagram.

16) If an object is placed at a distance of 8 cm from a concave mirror of focal length 10 cm, discuss the nature of the image formed by drawing the ray diagram.

Ans:

Given that focal length of concave mirror is 10cm and the object is placed at a distance of 8cm from the concave mirror. That means the object is placed between pole P and focus F of the concave mirror.

And we know that, when the object is placed between pole P and focus F of the concave mirror then the image will be formed behind the mirror which is virtual, erect and magnified as shown in following figure.

17) Draw a ray diagram showing how a concave mirror can be used to produce a real, inverted and diminished image of an object.

Ans:

When the object is placed beyond the centre of curvature C of the concave mirror then the image formed will be between focus F and centre of curvature C of the mirror and which is real, inverted and finished as shown in figure below.

When the object is placed at infinity from the concave mirror then the image is formed at the focus which is real, inverted and highly diminished as shown in figure below.

18.) Which mirror is used as a torch reflector? Draw a labelled diagram to show how a torch reflector can be used to produce a parallel beam of light. Where is the bulb placed in relation to the torch reflector?

Ans:

Concave mirrors are used as a torch reflector. In this case, the bulbs is placed at the focus of concave reflector which produces the powerful beam of parallel rays. Due to which we can see the objects which are at a certain distance in darkness of night also.

The following figure shows the formation of parallel beam of rays when the bulb is placed at the focus of the concave mirror reflector in torches.

19.) State where an object must be placed so that the image formed by a concave mirror is:
(a) erect and virtual.
(b) at infinity.
(c) the same size as the object.

Ans:

a)To obtain the image which is virtual and erect in case of concave mirror we have to place the object between pole P and focus F of the concave mirror.

b)To obtain the image at infinity we have to place the object at focus of the concave mirror.

c)To obtain the image having size same as that of the object we have to place the object at the centre of curvature of concave mirror.

20.) With the help of a labelled ray diagram, describe how a converging mirror can be used to give an enlarged upright image of an object.

Ans:-

When the object is placed between the pole P and focus F of the concave mirror then the image will be formed behind the mirror which is upright magnified, virtual and erect as shown in the following figure.

21) Make labelled ray diagrams to illustrate the formation of:

(a) a real image by a converging mirror.

(b) a virtual image by a converging mirror. Mark clearly the pole, focus, centre of curvature and position of object in each case.

Ans:

When the object is placed at the focus of the concave mirror them image formed will be at infinity, real, inverted and highly magnified as shown in the following figure.

When the object is placed between focus F and centre of curvature C of the concave mirror then the image will be formed behind the centre of curvature C which is real, inverted and magnified as shown in figure.

When the object is placed at the centre of curvature C of a concave mirror then the image will be formed at the centre of curvature which is real, inverted and of the same size as that of the object.

When the object is placed beyond the centre of curvature C of a concave mirror then the image will be formed between focus F and centre of curvature C of the mirror which is real, inverted and diminished as shown in the following figure.

When the object is placed at the infinity of the from the concave mirror at the focus F then the image will be formed at the focus F which is real, inverted and highly diminished as shown in following figure.

When the object is placed between pole P and focus F of concave mirror then the image will be formed behind the mirror which is virtual, erect and magnified as shown in figure.

22.) Briefly describe how you would find the focal length of a concave mirror quickly but approximately.

Ans:

When the object is at certain distance or at infinity from a concave mirror then there will be image formed at the focus. This fact is used to find out focal length of concave mirror quickly and approximately.
By using this fact, we can focus the objects like a window or tree on a screen with the help of concave mirror whose focal length is we have to determined.
The sharp image of the window or tree is formed at the focus of the concave mirror. And the distance of the image from the concave mirror gives the focal length of the concave mirror.

23.) Which type of mirror is used in a solar furnace? Support your answer with reason.

Ans:

Large concave mirrors are used in the field of solar energy in order to focus the solar rays for heating purpose of furnaces.
In this case, the solar furnace is placed at the focus of the large concave reflector. The concave mirror reflector helps in focusing the sun rays on the furnace and hence the solar furnace gets heated too to a temperature even steel may melt in the solar furnace.

24.) Name the type of mirror used by dentists. How does it help?

Ans:

Concave mirrors are used by dentist to see the large image of the teeth of the patients.
This happens when the tooth is at the focus of the concave mirror then we can see the enlarged image the tooth in the concave mirror. Hence, doctor may detect the defect in tooth easily.
These concave mirrors used by dentist are very small in size and they are fitted in a frame with the help of long handle.

25. Explain why, concave mirrors are used as shaving mirrors.

Ans:

Concave mirrors are used as shaving mirrors to see the large image of the face in the mirror.
This happens when the face is at the focus of concave mirror then the enlarged image of the face is seen in the concave mirror.
Due to which it helps in making smooth shaving. Hence concave mirrors are used as shaving mirrors.

26. Give two uses of concave mirrors. Explain why you would choose concave mirrors for these uses.

Ans:

Following are the uses of concave mirror:

Concave mirrors are used as shaving mirrors to see the large image of the face in the mirror.
This happens when the face is held within the focus of concave mirror then the enlarged image of the face is seen in the concave mirror.
Due to which it helps in making smooth shaving. Hence concave mirrors are used as shaving mirrors.
Concave mirrors are used by dentist to see the large image of the teeth of the patients.
This happens when the tooth is at the focus of the concave mirror then we can see the enlarged image the tooth in the concave mirror. Hence, doctor may detect the defect in tooth easily.
These concave mirrors used by dentist are very small in size and they are fitted in a frame with the help of long handle.

Long Answer Type Questions

27. (a) Draw ray-diagrams to show the formation of images when the object is placed in front of a concave mirror (converging mirror):

(i) between its pole and focus

(ii) between its centre of curvature and focus Describe the nature, size and position of the image formed in each case.

(b) State one use of concave mirror based on the formation of image as in case (i) above.

Ans:

i) when the object is placed between the pole P and focus F of the concave mirror then the image will be formed behind the mirror which is virtual, erect and magnified as shown in figure below.

ii) when the object is placed between the centre of curvature C and focus F of the mirror then the image will be formed beyond the centre of curvature which is real, inverted and magnified as shown in figure below.

Concave mirrors are used as shaving mirrors to see the large image of the face in the mirror.
This happens when the face is held within the focus of concave mirror then the enlarged image of the face is seen in the concave mirror.
Due to which it helps in making smooth shaving. Hence concave mirrors are used as shaving mirrors.

28) (a) Give two circumstances in which a concave mirror can form a magnified image of an object placed in front of it. Illustrate your answer by drawing labelled ray diagrams for both.

(b) Which one of these circumstances enables a concave mirror to be used as a shaving mirror?

Ans:

Following are the ways in which concave mirror can form the magnified image of an object.

When the object is placed between focus F and centre of curvature C of a concave mirror then the image will be formed beyond the centre of curvature which is real, inverted and magnified as shown in following figure.

When the object is placed at the focus of concave mirror then the image will be formed at infinity which is real, inverted and highly magnified as shown in figure below.

When the object is placed between pole P and focus F of the concave mirror then the image will be formed behind the mirror which is virtual, erect and magnified as shown in figure.

Concave mirrors are used as shaving mirrors to see the large image of the face in the mirror.
This happens when the face is held within the focus of concave mirror then the enlarged image of the face is seen in the concave mirror.
Due to which it helps in making smooth shaving. Hence concave mirrors are used as shaving mirrors.

Sign Conventions for Spherical Mirror:

Very Short Answer Type Questions:-

1.) According to the “New Cartesian Sign Convention” for mirrors, what sign has been given to the focal length of: (i) a concave mirror? (ii) a convex mirror?

Ans:

1) The focal length of concave mirror is considered as negative.

2) The focal length of convex mirror is considered as positive.

2.) Which type of mirror has: (a) positive focal length? (b) negative focal length?

Ans:

a)The mirror having positive focal length is the convex mirror.

b)The mirror having negative focal length is the concave mirror.

3.) What is the nature of a mirror having a focal length of, +10 cm?

Ans:

As the focal length is positive hence the mirror will be convex mirror.

4.) What kind of mirror can have a focal length of, – 20 cm?
Ans:

Since the focal length is negative hence the mirror will be concave mirror.

5.) Complete the following sentence:

Ans:

All the distances are measured from the pole of a spherical mirror.

6.) What sign (+ve or –ve) has been given to the following on the basis of Cartesian Sign Convention?
(a) Height of a real image.
(b) Height of a virtual image.

Ans:

a)The height of all the real and inverted images is taken as negative.

b)The height of all the virtual and inverted images is taken as negative.

Short Answer Type Questions:

7.) Describe the New Cartesian Sign Convention used in optics. Draw a labelled diagram to illustrate this sign convention.

Ans:

Fig. sign conventions for spherical mirrors

The sign conventions for reflection by spherical mirror are as follows:

All the distances are measured from the pole P of the mirror.
All the distances measured to the right of pole are taken as positive while the distances measured to the left of pole are taken as negative.
Distances measured above & normal to principal axis are taken as positive.
Distances measured below & normal to principal axis are taken as negative.
If the image is real then image distance is taken as negative.
If the image is virtual then the image distance is taken as positive.
Focal length of concave mirror is negative while the focal length of convex mirror is positive.
The figure given above explains the sign conventions in case of spherical mirrors

8) Giving reasons, state the ‘signs’ (positive or negative) which can be given to the following: (a) object distance (u) for a concave mirror or convex mirror

(b) image distances (v) for a concave mirror

(c) image distances (v) for a convex mirror

Ans:

As the object is always placed to the left of the mirror always hence the object distance is taken as always negative.
If the image is formed behind the concave mirror,then the image distance is taken as positive. And if the image is formed in front of the mirror, then the image distance will be taken as negative.

In case of convex mirror as the image is always formed on the right-hand side of the mirror hence the image distance for a convex mirror will be always positive.

Mirror Formula

Very Short Answer Type Questions

1.) If the magnification of a body of size 1 m is 2, what is the size of the image?

Ans:

If the magnification of a body of size 1m is 2 then the size of the image will be 2m.

2.) What is the position of the image when an object is placed at a distance of 20 cm from a concave mirror of focal length 20 cm?

Ans:

Since given that the image is formed when the object is at a distance of 20cm from a concave mirror having focal length 20cm.
That means the object is placed at the focus of the concave mirror and we know that when the object is placed at the focus F of the concave mirror then the image will be formed at infinity.

3.) What is the nature of image formed by a concave mirror if the magnification produced by the mirror is (a) + 4, and (b) – 2?

Ans:

a) When the magnification has positive value that means the image formed will be virtual and erect.

b) When the magnification has negative value that means the image formed will be real and inverted.

4.) State the relation between object distance, image distance and focal length of a spherical mirror (concave mirror or convex mirror).

Ans:

The relationship between object distance u, image distance v and the focal length f of the spherical mirror is given by
1/f = 1/u + 1/v

This formula is knowing as mirrors formula.

5.) Write the mirror formula. Give the meaning of each symbol which occurs in it.

Ans:

The mirrors formula is given by
1/f = 1/u + 1/v

Where, f is the focal length of the spherical mirror
u is the object distance
v is the image distance

6.) What is the ratio of the height of an image to the height of an object known as?

Ans:

The ratio of the height of an image to the height of the object is known as linear magnification which is given by
Magnification = height of the image/ height of the object
Thus, m= h2/ h1

7.) Define linear magnification produced by a mirror.

Ans:

The ratio of the height of an image to the height of the object is known as linear magnification which is given by
Magnification = height of the image/ height of the object
Thus, m= h2/ h1

8.) Write down a formula for the magnification produced by a concave mirror.

(a) in terms of height of object and height of image

(b) in terms of object distance and image distance

Ans:

a) The magnification produced by the concave mirror in terms of height of objecth1 and height of image h2 is given by,
Magnification m = h2/ h1

b) The magnification produced by convex mirror in terms of the object distance u and image distance v is given by,
Magnification m= -v/u

9.) Describe the nature of image formed when the object is placed at a distance of 20 cm from a concave mirror of focal length 10 cm.

Ans:

When the object is placed at a distance of 20cm from a concave mirror of focal length 10cm then the nature of the image formed will be real and inverted.

10.) Fill in the following blanks with suitable words:

Ans:

a) If the magnification has a plus sign, then the image is virtual and erect.
b) If the magnification has a minus sign, then the image is real and inverted.

Short Answer Type Questions

11.) An object is placed at a distance of 10 cm from a concave mirror of focal length 20 cm.

(a) Draw a ray diagram for the formation of image.
(b) Calculate the image distance.
(c) State two characteristics of the image formed.

Ans:

a) The following is the ray diagram for the formation of image as given above.

b) Given that, object distance u = 10cm, focal length f = 20cm
We know that, the mirrors formula is given by,
1/f = 1/v + 1/u
1/v = 1/f – 1/u
1/v = 1/20 – 1/10 = (1-2)/20 = -1/20
Thus, v = -20cm
Thus, the image distance will be 20cm.

c) The image formed will be virtual, erect and magnified.

12.) If an object of 10 cm height is placed at a distance of 36 cm from a concave mirror of focal length 12 cm, find the position, nature and height of the image.

Ans:

Given that,
Object height h1 = 10cm
Object distance u = 36cm
Focal length f = 12cm

We know that, mirrors formula is given by

1/f = 1/u + 1/v
1/v = 1/f – 1/u

= 1/12 – 1/36

= 2/36

= 1/18
Thus, v = 18cm

The magnification produced is given by,
M = -v/u = h2/h1
-18/36= h2/ 10
Thus,

h2 = -18/36*10

= -1/2*10= -5 cm

Thus, the image will be formed in front of the concave mirror which is at distance of 18cm from the mirror.
The image formed is real and inverted having height as 5cm.

13.) At what distance from a concave mirror of focal length 10 cm should an object 2 cm long be placed in order to get an erect image 6 cm tall?

Ans:

Given that,
Focal length f= -10cm
Object height h1 = 2cm
Image height h2 = 6cm

We know that,
Magnification m = h2/ h1 = 6/2 = 3
But, -v/u = m = 3
Thus, v = -3u

We know that,
1/f = 1/v + 1/u
-1/10 = -1/3u + 1/u = 2/3u
Thus, 3u/2 = -10
Hence, 3u = -20
And u = -6.66 cm

Thus, the object is placed at a distance of 6.66cm on the left side of the mirror.

14.) When an object is placed at a distance of 15 cm from a concave mirror, its image is formed at 10 cm in front of the mirror. Calculate the focal length of the mirror.

Ans:

Given that,
Object distance u =+15cm
Image distance v = 10cm

We know that,
1/f = 1/v + 1/u = 1/10 + 1/15 = 25/ 150 = 5/30 = 1/6
Thus, f = 6cm
Hence the focal length of the mirror is 6cm

15.) An object 3 cm high is placed at a distance of 8 cm from a concave mirror which produces a virtual image 4.5 cm high:
(i) What is the focal length of the mirror?
(ii) What is the position of image?
(iii) Draw a ray-diagram to show the formation of image.

Ans:
Given that,

Object height h1= 3cm
Object distance u = 8cm
Image height h2 = 4.5 cm

1) We know that,
Magnification m= -v/u = h2/ h1
-v/8 = 4.5/3 = 1.5
Thus, v= -1.5*8= -12cm

And mirrors formula is given by,
1/f = 1/u + 1/v
1/f= 1/8 -1/12 = 4/96= 1/24
Thus, f= 24cm
Thus, the focal length of the mirror is 24cm.

2) The position of the image is 12cm behind the concave mirror.

3) The following diagram shows the formation of image as discussed above.

16.) A converging mirror forms a real image of height 4 cm of an object of height 1 cm placed 20 cm away from the mirror:
(i) Calculate the image distance.
(ii) What is the focal length of the mirror?

Ans:

Given that,
Image height h2 = 4cm
Object height h1 = 1cm
Object distance u = 20cm

1)We know that,
Magnification m = -v/u = h2/ h1
-v/20= 4/1
Thus, v = -20*4= -80cm
Thus, the image distance is 80 cm.

2)The focal length of the mirror is given by,
1/f = 1/u + 1/v
1/f = 1/20 + 1/80 = 5/80= 1/16
Thus, f = 16cm

Thus, the focal length of the lens is 16cm.

17.) An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed so that a sharp focused image can be obtained? Find the size and nature of image. [Hint. Find the value of image distance (v) first. The screen should be placed from the mirror at a distance equal to image distance].

Ans:

Given that,

Object height h1 = 7cm
Object distance u= 27cm
Focal length f = 18cm

We know that,
1/f = 1/u + 1/v
1/v = 1/f – 1/u = 1/18 – 1/27
3/v = 1/6 – 1/9
9/v = ½ – 1/3
9/v = 1/6
Thus, v = 6*9= 54cm

Thus, the screen should be placed at a distance of 54cm in front of the concave mirror.

Also, we know that
Magnification m= -v/u = h2/h1
-54/27= h2/7
-2 = h2/7
Thus, h2 = -2*7 = -14cm

Thus, the height of the image is 14cm which is real and inverted.

18.) An object 3 cm high is placed at a distance of 10 cm in front of a converging mirror of focal length 20 cm. Find the position, nature and size of the image formed.
Ans:

Given that,
Object height h1 = 3cm
Object distance u= 10cm
Focal length f= 20cm
We know that,
1/f = 1/v + 1/u
1/v = 1/f – 1/u
1/v = 1/20 – 1/10 = -1/20
Thus, v = -20cm
Thus, the image is formed at a distance of 20cm behind the converging mirror.

Also,
Magnification m= -v/u = h2/ h1
20/10= h2/3
Thus, h2 = 2*3= 6cm

The height of the image is 6cm which is virtual and erect.

19.) A concave mirror has a focal length of 4 cm and an object 2 cm tall is placed 9 cm away from it. Find the nature, position and size of the image formed.
Ans:

Given that,
Focal length f= 4cm
Object height h1 = 2cm
Object distance u= 9cm
We know that,
1/f = 1/u + 1/v
1/v = 1/f -1/u = ¼ – 1/9 = 5/36
Thus, v = 36/5 = 7.2 cm
Thus, the image will be formed at a distance of 7.2 cm in front of the mirror.

Also,
Magnification m= -v/u = h2/ h1
-7.2/9= h2/ 2
Thus, h2 = – 7.2*2)/9 = -14.4/9 = -1.55 = -1.6cm
Thus, the height of the image is 1.6cm
Thus, the image formed will be real and inverted.

20.) When an object is placed 20 cm from a concave mirror, a real image magnified three times is formed.

Find:-

(a) the focal length of the mirror.
(b) Where must the object be placed to give a virtual image three times the height of the object?

Ans:

Given that,
Object distance u = -20cm
Magnification m= 3
a)We know that, the magnification is given by
M = -v/u
-3= -v/-20
Thus, v = -60cm

Hence, the focal length of the mirror is,
1/f = 1/u + 1/v = -1/20 – 1/60= -4/60 = -1/15
Thus, f = -15cm
Hence the focal length of the mirror is 15cm.

b) Given that,

h2 = 3h1
Thus, m = h2/ h1 = -v/u = 3
Hence, v = -3u

We know that,
1/f = 1/u + 1/v = 1/u -1/3u = 2/3u
Thus, f = 3u/2
Hence, u = 2/3*f = 2/3*15= 10cm

Thus, the object should be placed at a distance of 10cm from the concave mirror.

21.) A dentist’s mirror has a radius of curvature of 3 cm. How far must it be placed from a small dental cavity to give a virtual image of the cavity that is magnified five times ?

Ans:

Given that,
For concave mirror,
R= -3cm
Focal length f = R/2 = -3/2 = -1.5cm
Also given that, magnification is m=5
We know that, m = -v/u = 5
Thus, v = -5u
We know that,
1/f = 1/u + 1/v = 1/u -1/5u = 4/5u
Thus, f = 5u/4
And u = 4/5*f = 4/5*(-1.5) = -1.2cm
Thus, the dentist must have to place the mirror at a distance of 1.2cm from the dental cavity.

22.) A large concave mirror has a radius of curvature of 1.5 m. A person stands 10 m in front of the mirror. Where is the person’s image?

Ans:

Given that,

R =- 1.5m
Object distance u = -10m
Focal length f = R/2 = -1.5/2 = – 0.75cm

We know that,
1/f = 1/u + 1/v
1/v = 1/f – 1/u = -2/1.5 + 1/10 = -1.33 + 0.1 = -1.23

Thus, v = -0.81 m
Hence, the image will be formed at a distance of 0.81m in front of the concave mirror.

23.) An object of 5.0 cm size is placed at a distance of 20.0 cm from a converging mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed to get the sharp image? Also calculate the size of the image.

Ans:

Given that,

Object height h1 = 5cm
Object distance u = -20cm
Focal length f = -15cm
Image distance v= ?
Image height h2 = ?

We know that,
1/f = 1/u + 1/v
1/v = 1/f – 1/u = -1/15 + 1/20
5/v = -1/3 + ¼
5/v = -1/12

Thus, v = -12*5= -60cm
Hence, the object is placed at a distance of 60cm in front of the mirror.

Also, m = -v/u = h2/h1
Hence, -60/20= h2/ 5
Thus, h2 = -3*5= -1.5cm

The height of the object is 1.5cm.

24.) A concave mirror produces three times enlarged virtual image of an object placed at 10 cm in front of it. Calculate the radius of curvature of the mirror.

Ans:

Given that,

Magnification m = 3
Object distance u = -10cm
R=?

We know that,
Magnification m = -v/u
Thus, 3 = -v/-10 = v/10
Hence, v = 30cm

Also, 1/f = 1/u + 1/v = -1/10 + 1/30 = -2/30 = -1/15
Thus, f = -15cm
And radius of curvature is given by,
R = 2f = 2*(-15) = -30cm

Thus, the radius of curvature is 30cm

25.) A bright object 50 mm high stands on the axis of a concave mirror of focal length 100 mm and at a distance of 300 mm from the concave mirror. How big will the image be?

Ans:

Given that,
Object height h1 = 50mm
Focal length f = -100mm
Object distance u = -300mm
We know that,
1/f = 1/u + 1/v
1/v = 1/f –1/u
1/v = 1/-100 + 1/300 = -2/300 = -1/150
Thus, v = -150mm
Also, magnification m = h2/h1 = -v/u
Thus, h2/50 =- 150/300
Thus, h2 = ½*50= 25 mm
Thus, the height of the image will be 25mm.

26.) How far should an object be placed from the pole of a converging mirror of focal length 20 cm to form a real image of the size exactly 1/4 th the size of the object?

Ans:

Given that,

Focal length f = -20cm
Magnification m = -1/4

We know that,
Magnification m = -v/u = -1/4

Thus, v = u/4
Also, we know that,
1/f = 1/u + 1/v = 1/u + 4/u = 5/u

Thus, f = u/5
And u = 5*f = 5*(-20)= -100cm

Thus, the object should be placed at a distance of 100cm from the pole of the converging mirror.

27.) When an object is placed at a distance of 50 cm from a concave spherical mirror, the magnification produced is, – 1 2. Where should the object be placed to get a magnification of, 1 5 – ?

Ans:-

Given that,

Object distance u = -50cm
Magnification m = -1/2
What is u when m= -1/5.

We know that,
Magnification m = -v/u
-1/2= -v/-50
1/2= -v/50
Thus, v = -1/2*50= -25 cm
Now, 1/f = 1/u + 1/v
1/f = 1/-50 -1/25 = -3/50
Thus, f = -50/3 cm
Now, when m = -1/5 and v = -mu then u=?

We have 1/f = 1/u + 1/v
-3/50 = 1/u -1/mu
-3/50= 1/u +5/u = 6/u

Thus, u/6 = -50/3
And u = -50/3*6= -100cm

Thus, to get the magnification m = -1/5 the object should have to place at a distance of 100cm from the concave mirror.

28.) An object is placed (a) 20 cm, (b) 4 cm, in front of a concave mirror of focal length 12 cm. Find the nature and position of the image formed in each case.

Ans:

a) Given that,
Object distance u = -20cm
Focal length f = -12cm

We know that,
1/f = 1/u + 1/v
1/v = 1/f – 1/u = -1/12 + 1/20
2/v = -1/6 + 1/10
4/v = -1/3 + 1/5
4/v = -2/15
V/4 = -15/2

Thus, v = -15/2*4= -30cm

Thus, the image will be formed at a distance of 30cm in front of the mirror.
Magnification m = -v/u = 30/-20= -3/2= -1.5

Thus, the image formed will be real inverted and magnified.

b) Given that,
Object distance u = – 4cm
Focal length f= – 12cm

We know that,
1/f = 1/u +1/v
1/v = 1/f – 1/u
1/v = -1/12 + ¼ = 2/12 = 1/6

Thus, v = 6cm
Thus, the image will be formed at a distance of 6cm behind the mirror.
Magnification m = -v/u = -6/-4= 3/2= 1.5cm

Thus, the image formed will be virtual and erect.

29.) A concave mirror produces a real image 1 cm tall of an object 2.5 mm tall placed 5 cm from the mirror. Find the position of the image and the focal length of the mirror.

Ans:

Given that,

Height of image h2= -1cm
Object height h1= 2.5mm = 0.25cm
Object distance u= -5cm

We know that,
Magnification m = h2/h1 = -v/u
Thus, -1/0.25= v/5
Thus, v= -1/0.25*5= -20cm

Thus, the image will be formed at a distance of 20cm in front of the mirror.

We have, 1/f = 1/u + 1/v
1/f = -1/5 -1/20 = -5/20= -1/4
Thus, f = -4cm

Thus, the focal length of the concave mirror is 4cm

30.) A man holds a spherical shaving mirror of radius of curvature 60 cm, and focal length 30 cm, at a distance of 15 cm, from his nose. Find the position of image, and calculate the magnification.

Ans:

Given that,

Radius of curvature R= 60cm
We know, R= 2f
And F = R/2 = 60/2 = 30cm
Focal length f = -30cm
Object distance u = -15cm

We know that,
1/f = 1/u + 1/v

1/v = 1/f -1/u = -1/30 +1/15= 1/30
Thus, v = 30cm

Thus, the image will be formed at a distance of 30cm behind the mirror.
And magnification m = -v/u = -30/-15= 2

Thus, the image formed is 2 times magnified than the object.

Long Answer Type Question

31.) (a) An object is placed just outside the principal focus of concave mirror. Draw a ray diagram to show how the image is formed, and describe its size, position and nature.

(b) If the object is moved further away from the mirror, what changes are there in the position and size of the image?

(c) An object is 24 cm away from a concave mirror and its image is 16 cm from the mirror. Find the focal length and radius of curvature of the mirror, and the magnification of the image.

Ans:

a) When the object is placed just outside the focus F means the object is placed between focus F and centre of curvature C of the concave mirror as shown in figure then the image formed is beyond the centre of curvature of the concave mirror.
And the image formed is real, inverted and magnified as shown in figure below.

If the object is moved further away from the mirror, then the image will be formed nearer to the mirror and whose size goes on decreasing also.

Given that,

Object distance u = -24cm

Image distance v = -16cm

We know that,

1/f = 1/u + 1/v

1/f = -1/24 – 1/16

4/f = -1/6 – ¼

8/f = -1/3 – ½

8/f = -5/6

Thus, f/8 = -6/5

And F = -6/5*8= -48/5= -9.6cm

Thus, the focal length of the concave mirror is 9.6cm.

And R = 2f = 2*9.6= 19.2cm

Thus, the radius of curvature is 19.2cm

And magnification m = -v/u = 16/-24= – 4/6= -2/3= -0.66

Thus, the magnification produced is 0.66.

Rules For Obtaining Images Formed by Convex Mirror

Very Short Answer Type Questions

1.) Ans

a)The images formed by a convex mirror are virtual and erect.

b)The images formed by a concave mirror are virtual and erect, also real and inverted.

2.) Ans:

Convex mirrors have a wider field of view.

3.) Ans:

To see an enlarged image of our face we have to use concave mirror.

4.) Ans:

Convex mirror always produces a virtual, erect and diminished image of an object.

5.) Ans:

Given that,

R= 30cm
We know, R= 2f
Thus, f = R/2 = 30/2= 15cm
We know that, 1/f = 1/u + 1/v

Here u = infinity
1/f = 1/v
Thus, v = f = 15cm

Thus, the image will be formed at the focus at a distance of 15cm behind the convex mirror.

6.) Ans:

The spherical mirror which produces a real and diminished image of an object is the concave mirror.

7.) Ans:

The spherical mirror which produces a virtual and diminished image of an object is the convex mirror.

8.) Ans:

To see a magnified image of an object in a mirror the person should have to use a concave mirror.

9.) Ans:

a)Concave mirror gives an erect and enlarged image of an object.

b)Convex mirror gives an erect and diminished image of an object.

10.) Ans:

The above statement is true.

Since, convex mirror is the diverging mirror which is used as a rear-view mirror.

11.) Ans:

a)Concave mirror is used as a shaving mirror.

b) Big Convex mirror is used as a shop security mirror.

12.) Ans:

Convex mirrors are usually used as a rear-view mirror in motor car.

13.) Ans:-

Convex mirrors are used in big shopping centres to watch the activities of the customers.

14.) Ans:

The ray of light directed towards the focal point in case of convex lens also be reflected as a parallel ray to principal axis as in figure below.

15) Fill in the following blank with a suitable word:

Ans:

A ray of light which is parallel to the principal axis of a convex mirror, appears to be coming from focus after reflection from the mirror.

Short Answer Type Questions

16) Ans:-

A driver prefers to use a convex mirror as rear-view mirror because of the following two main reasons:

A convex mirror always produces an erect image of the object
The image which is formed in the convex mirror is highly diminished due to which it helps in seeing a wide field of view.

The convex mirror allows the driver to see the large area of traffic behind him which is not possible with the plane mirror. Hence, to see the traffic or vehicles coming from behind in order to get safe driving drivers prefers to use a convex mirror as a real-view mirror in a vehicle.

17) Ans:

Because concave mirror produces the inverted image of the object which is at a distant apart from it. If concave mirrors are used as rear-view mirror in cars, then we see in concave mirror that all the vehicles are on the road are running upside down with their wheels in the air.
So it does not help the drivers while driving. Hence concave mirrors are not used as a rear-view mirror in vehicles.

18) Ans:

When the object is placed between pole P and infinity of a convex mirror then the image will be formed behind the mirror between pole P and focus F.

The image formed will be virtual, erect and diminished as shown in figure below

When the object is placed at infinity from the convex mirror then the image will be formed behind the mirror at the focus F.

The image formed will be virtual, erect and highly diminished as shown in figure below.

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Lakhmir Singh Class 10 Physics 4th Chapter Reflection of Light PDF Solution

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