Page 168
Ans: 1
Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.
Ans: 2
Radius of curvature, R= 20 cm
Radius of curvature of a spherical mirror = 2 × Focal length (f)
R= 2f
Hence,the focal length of the given spherical mirror is 10 cm.
Ans: 3
When an object is placed between the pole and the principal focus of a concave mirror, the image formed is virtual, erect, and enlarged.
Ans: 4
Convex mirrors give a virtual, erect, and diminished image of the objects placed in front of them. They are preferred as a rear-view mirror in vehicles because they give a wider field of view, which allows the driver to see most of the traffic behind him.
Page 171
Ans: 1
Radius of curvature, R= 32 cm
Radius of curvature = 2 × Focal length (f)
R= 2f
Hence,the focal length of the given convex mirror is 16 cm.
Ans: 2
Magnification produced by a spherical mirror is given by the relation,
Let the height of the object, ho= h
Then, height of the image, hI= −3h (Image formed is real)
Object distance, u= −10 cm
v= 3 × (−10) = −30 cm
Here, the negative sign indicates that an inverted image is formed at a distance of
30 cm in front of the given concave mirror.
Page 176
Ans: 1
The light ray bends towards the normal.
When a ray of light travels from an optically rarer medium to an opticallydenser medium, it gets bent towards the normal. Since water is optically denser than air, a ray of light travelling from air into the water will bend towards the normal.
Ans: 2
Refractiveindex of a medium nmis given by,
Speed of light in vacuum, c= 3 × 108 m s−1
Refractive index of glass, ng= 1.50
Speedof light in the glass,
Ans: 3
Highest optical density = Diamond
Lowest optical density = Air
Optical density of a medium is directly related with the refractive index of that medium. A medium which has the highest refractive index will have the highest optical density and vice-versa.
It can be observed from table 10.3 that diamond and air respectively have the highest and lowest refractive index. Therefore, diamond has the highest optical density and air has the lowest optical density.
Ans: 4
Speed of light in a medium is given by the relation for refractive index (nm). The relation is given as
It can be inferred from the relation that light will travel the slowest in the material which has the highest refractive index and travel the fastest in the material which has the lowest refractive index.
It can be observed from table 10.3 that the refractive indices of kerosene, turpentine, and water are 1.44, 1.47, and 1.33 respectively. Therefore, light travels the fastest in water.
Ans: 5
Refractive index of a medium nmis related to the speed of light in that medium vby the relation:
Where, c is the speed of light in vacuum/air
The refractive index of diamond is 2.42. This suggests that the speed of light in diamond will reduce by a factor 2.42 compared to its speed in air.
Page 184
Ans: 1
Powerof lens is defined as the reciprocal of its focal length. If Pis the power of a lens of focal length Fin metres, then
The S.I. unit of power of a lens is Dioptre. It is denoted by D.
1dioptre is defined as the power of a lens of focal length 1 metre.
∴1 D = 1 m−1
Ans: 2
When an object is placed at the centre of curvature, 2F1, of a convex lens, its image is formed at the centre of curvature, 2F2, on the other side of the lens. The image formed is inverted and of the same size as the object, as shown in the given figure.
It is given that the image of the needle is formed at a distance of 50 cm from the convex lens. Hence, the needle is placed in front of the lens at a distance of
50 cm.
Object distance, u= −50 cm
Image distance, v= 50 cm
Focal length = f
According to the lens formula,
Hence, the power of the given lens is +4 D.
Ans: 3
Focal length of concave lens, f= 2 m
Here, negative sign arises due to the divergent nature of concave lens.
Hence,the power of the given concave lens is −0.5 D.
Page 185
Ans: 1
(d) A lens allows light to pass through it. Since clay does not show such property, it cannot be used to make a lens.
Ans: 2
(d) When an object is placed between the pole and principal focus of a concave mirror, the image formed is virtual, erect, and larger than the object
Ans: 3
(b) When an object is placed at the centre of curvature in front of a convex lens, its image is formed at the centre of curvature on the other side of the lens. The image formed is real, inverted, and of the same size as the object.
Ans: 4
(a) By convention, the focal length of a concave mirror and a concave lens are taken as negative. Hence, both the spherical mirror and the thin spherical lens are concave in nature.
Page 186
Ans: 5
(d) A convex mirror always gives a virtual and erect image of smaller size of the object placed in front of it. Similarly, a plane mirror will always give a virtual and erect image of same size as that of the object placed in front of it. Therefore, the given mirror could be either plane or convex.
Ans: 6
(c) A convex lens gives a magnified image of an object when it is placed between the radius of curvature and focal length. Also, magnification is more for convex lenses having shorter focal length. Therefore, for reading small letters, a convex lens of focal length 5 cm should be used.
Ans: 7
Range of object distance = 0 cm to15 cm
A concave mirror gives an erect image when an object is placed between its pole (P) and the principal focus (F).
Hence, to obtain an erect image of an object from a concave mirror of focal length 15 cm, the object must be placed anywhere between the pole and the focus. The image formed will be virtual, erect, and magnified in nature, as shown in the given figure.
Ans: 8
(a) Concave (b) Convex (c) Concave
Explanation
(a) Concave mirror is used in the headlights of a car. This is because concave mirrors can produce powerful parallel beam of light when the light source is placed at their principal focus.
(b) Convex mirror is used in side/rear view mirror of a vehicle. Convex mirrors give a virtual, erect, and diminished image of the objects placed in front of it. Because of this, they have a wide field of view. It enables the driver to see most of the traffic behind him/her.
(c) Concave mirrors are convergent mirrors. That is why they are used to construct solar furnaces. Concave mirrors converge the light incident on them at a single point known as principal focus. Hence, they can be used to produce a large amount of heat at that point.
Ans: 9
The convex lens will form complete image of an object, even if its one half is covered with black paper. It can be understood by the following two cases.
Case I
When the upper half of the lens is covered
In this case, a ray of light coming from the object will be refracted by the lower half of the lens. These rays meet at the other side of the lens to form the image of the given object, as shown in the following figure.
Case II
When the lower half of the lens is covered
In this case, a ray of light coming from the object is refracted by the upper half of the lens. These rays meet at the other side of the lens to form the image of the given object, as shown in the following figure.
Ans: 10
Object distance, u= −25 cm
Object height, ho= 5 cm
Focal length, f= +10 cm
According to the lens formula,
The positive value of vshows that the image is formed at the other side of the lens.
The negative sign shows that the image is real and formed behind the lens.
The negative value of image height indicates that the image formed is inverted.
The position, size, and nature of image are shown in the following ray diagram.
Ans: 11
Focal length of concave lens (OF1),f = −15 cm
Image distance, v= −10 cm
According to the lens formula,
The negative value of uindicates that the object is placed 30 cm in front of the lens. This is shown in the following ray diagram.
Ans: 12
Focal length of convex mirror, f= +15 cm
Object distance, u= −10 cm
According to the mirror formula,
The positive value of vindicates that the image is formed behind the mirror.
The positive value of magnification indicates that the image formed is virtual and erect.
Ans: 13
Magnification produced by a mirror is given by the relation
The magnification produced by a plane mirror is +1. It shows that the image formed by the plane mirror is of the same size as that of the object. The positive sign shows that the image formed is virtual and erect.
Ans: 14
Object distance, u= −20 cm
Object height, h= 5 cm
Radius of curvature, R= 30 cm
Radius of curvature = 2 × Focal length
R= 2f
f= 15 cm
According to the mirror formula,
The positive value of vindicates that the image is formed behind the mirror.
The positive value of image height indicates that the image formed is erect.
Therefore, the image formed is virtual, erect, and smaller in size.
Ans: 15
Object distance, u= −27 cm
Object height, h= 7 cm
Focal length, f =−18 cm
According to the mirror formula,
The screen should be placed at a distance of 54 cm in front of the given mirror.
The negative value of magnification indicates that the image formed is real.
The negative value of image height indicates that the image formed is inverted.
Ans: 16
A concave lens has a negative focal length. Hence, it is a concave lens.
Ans: 17
A convex lens has a positive focal length. Hence, it is a convex lens or a converging lens.
Ans: 1
Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.
Ans: 2
Radius of curvature, R= 20 cm
Radius of curvature of a spherical mirror = 2 × Focal length (f)
R= 2f
Hence,the focal length of the given spherical mirror is 10 cm.
Ans: 3
When an object is placed between the pole and the principal focus of a concave mirror, the image formed is virtual, erect, and enlarged.
Ans: 4
Convex mirrors give a virtual, erect, and diminished image of the objects placed in front of them. They are preferred as a rear-view mirror in vehicles because they give a wider field of view, which allows the driver to see most of the traffic behind him.
Page 171
Ans: 1
Radius of curvature, R= 32 cm
Radius of curvature = 2 × Focal length (f)
R= 2f
Hence,the focal length of the given convex mirror is 16 cm.
Ans: 2
Magnification produced by a spherical mirror is given by the relation,
Let the height of the object, ho= h
Then, height of the image, hI= −3h (Image formed is real)
Object distance, u= −10 cm
v= 3 × (−10) = −30 cm
Here, the negative sign indicates that an inverted image is formed at a distance of
30 cm in front of the given concave mirror.
Page 176
Ans: 1
The light ray bends towards the normal.
When a ray of light travels from an optically rarer medium to an opticallydenser medium, it gets bent towards the normal. Since water is optically denser than air, a ray of light travelling from air into the water will bend towards the normal.
Ans: 2
Refractiveindex of a medium nmis given by,
Speed of light in vacuum, c= 3 × 108 m s−1
Refractive index of glass, ng= 1.50
Speedof light in the glass,
Ans: 3
Highest optical density = Diamond
Lowest optical density = Air
Optical density of a medium is directly related with the refractive index of that medium. A medium which has the highest refractive index will have the highest optical density and vice-versa.
It can be observed from table 10.3 that diamond and air respectively have the highest and lowest refractive index. Therefore, diamond has the highest optical density and air has the lowest optical density.
Ans: 4
Speed of light in a medium is given by the relation for refractive index (nm). The relation is given as
It can be inferred from the relation that light will travel the slowest in the material which has the highest refractive index and travel the fastest in the material which has the lowest refractive index.
It can be observed from table 10.3 that the refractive indices of kerosene, turpentine, and water are 1.44, 1.47, and 1.33 respectively. Therefore, light travels the fastest in water.
Ans: 5
Refractive index of a medium nmis related to the speed of light in that medium vby the relation:
Where, c is the speed of light in vacuum/air
The refractive index of diamond is 2.42. This suggests that the speed of light in diamond will reduce by a factor 2.42 compared to its speed in air.
Page 184
Ans: 1
Powerof lens is defined as the reciprocal of its focal length. If Pis the power of a lens of focal length Fin metres, then
The S.I. unit of power of a lens is Dioptre. It is denoted by D.
1dioptre is defined as the power of a lens of focal length 1 metre.
∴1 D = 1 m−1
Ans: 2
When an object is placed at the centre of curvature, 2F1, of a convex lens, its image is formed at the centre of curvature, 2F2, on the other side of the lens. The image formed is inverted and of the same size as the object, as shown in the given figure.
It is given that the image of the needle is formed at a distance of 50 cm from the convex lens. Hence, the needle is placed in front of the lens at a distance of
50 cm.
Object distance, u= −50 cm
Image distance, v= 50 cm
Focal length = f
According to the lens formula,
Hence, the power of the given lens is +4 D.
Ans: 3
Focal length of concave lens, f= 2 m
Here, negative sign arises due to the divergent nature of concave lens.
Hence,the power of the given concave lens is −0.5 D.
Page 185
Ans: 1
(d) A lens allows light to pass through it. Since clay does not show such property, it cannot be used to make a lens.
Ans: 2
(d) When an object is placed between the pole and principal focus of a concave mirror, the image formed is virtual, erect, and larger than the object
Ans: 3
(b) When an object is placed at the centre of curvature in front of a convex lens, its image is formed at the centre of curvature on the other side of the lens. The image formed is real, inverted, and of the same size as the object.
Ans: 4
(a) By convention, the focal length of a concave mirror and a concave lens are taken as negative. Hence, both the spherical mirror and the thin spherical lens are concave in nature.
Page 186
Ans: 5
(d) A convex mirror always gives a virtual and erect image of smaller size of the object placed in front of it. Similarly, a plane mirror will always give a virtual and erect image of same size as that of the object placed in front of it. Therefore, the given mirror could be either plane or convex.
Ans: 6
(c) A convex lens gives a magnified image of an object when it is placed between the radius of curvature and focal length. Also, magnification is more for convex lenses having shorter focal length. Therefore, for reading small letters, a convex lens of focal length 5 cm should be used.
Ans: 7
Range of object distance = 0 cm to15 cm
A concave mirror gives an erect image when an object is placed between its pole (P) and the principal focus (F).
Hence, to obtain an erect image of an object from a concave mirror of focal length 15 cm, the object must be placed anywhere between the pole and the focus. The image formed will be virtual, erect, and magnified in nature, as shown in the given figure.
Ans: 8
(a) Concave (b) Convex (c) Concave
Explanation
(a) Concave mirror is used in the headlights of a car. This is because concave mirrors can produce powerful parallel beam of light when the light source is placed at their principal focus.
(b) Convex mirror is used in side/rear view mirror of a vehicle. Convex mirrors give a virtual, erect, and diminished image of the objects placed in front of it. Because of this, they have a wide field of view. It enables the driver to see most of the traffic behind him/her.
(c) Concave mirrors are convergent mirrors. That is why they are used to construct solar furnaces. Concave mirrors converge the light incident on them at a single point known as principal focus. Hence, they can be used to produce a large amount of heat at that point.
Ans: 9
The convex lens will form complete image of an object, even if its one half is covered with black paper. It can be understood by the following two cases.
Case I
When the upper half of the lens is covered
In this case, a ray of light coming from the object will be refracted by the lower half of the lens. These rays meet at the other side of the lens to form the image of the given object, as shown in the following figure.
Case II
When the lower half of the lens is covered
In this case, a ray of light coming from the object is refracted by the upper half of the lens. These rays meet at the other side of the lens to form the image of the given object, as shown in the following figure.
Ans: 10
Object distance, u= −25 cm
Object height, ho= 5 cm
Focal length, f= +10 cm
According to the lens formula,
The positive value of vshows that the image is formed at the other side of the lens.
The negative sign shows that the image is real and formed behind the lens.
The negative value of image height indicates that the image formed is inverted.
The position, size, and nature of image are shown in the following ray diagram.
Ans: 11
Focal length of concave lens (OF1),f = −15 cm
Image distance, v= −10 cm
According to the lens formula,
The negative value of uindicates that the object is placed 30 cm in front of the lens. This is shown in the following ray diagram.
Ans: 12
Focal length of convex mirror, f= +15 cm
Object distance, u= −10 cm
According to the mirror formula,
The positive value of vindicates that the image is formed behind the mirror.
The positive value of magnification indicates that the image formed is virtual and erect.
Ans: 13
Magnification produced by a mirror is given by the relation
The magnification produced by a plane mirror is +1. It shows that the image formed by the plane mirror is of the same size as that of the object. The positive sign shows that the image formed is virtual and erect.
Ans: 14
Object distance, u= −20 cm
Object height, h= 5 cm
Radius of curvature, R= 30 cm
Radius of curvature = 2 × Focal length
R= 2f
f= 15 cm
According to the mirror formula,
The positive value of vindicates that the image is formed behind the mirror.
The positive value of image height indicates that the image formed is erect.
Therefore, the image formed is virtual, erect, and smaller in size.
Ans: 15
Object distance, u= −27 cm
Object height, h= 7 cm
Focal length, f =−18 cm
According to the mirror formula,
The screen should be placed at a distance of 54 cm in front of the given mirror.
The negative value of magnification indicates that the image formed is real.
The negative value of image height indicates that the image formed is inverted.
Ans: 16
A concave lens has a negative focal length. Hence, it is a concave lens.
Ans: 17
A convex lens has a positive focal length. Hence, it is a convex lens or a converging lens.
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