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.
You are given kerosene, turpentine and water. In which of these does the light travel fastest? Use the information given in Table.
| Material medium | Refractive index | Material medium | Refractive index |
| Air | 1.0003 | Canada Balsam | 1.53 |
| Ice | 1.31 | ||
| Water | 1.33 | Rock salt | 1.54 |
| Alcohol | 1.36 | ||
| Kerosene | 1.44 | Carbon disulphide | 1.63 |
| Fused quartz | 1.46 | Dense flint glass | 1.65 |
| Turpentine oil | 1.47 | Ruby | 1.71 |
| Benzene | 1.50 | Sapphire | 1.77 |
Ans
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.
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,
Power of Lens P = 1/ f (metres)
= 1/ 2.5 =+4D
Hence, the power of the given lens is +4 D.
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.
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.
Object distance, u= - 25 cm
Object height, ho = 5 cm
Focal length, f= +10 cm
According to the lens formula,
The positive value of shows 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.
Real, inverted, diminished.
Focal length of concave lens (OF1), f = −15 cm
Image distance, v = −10 cm
According to the lens formula,
Focal length of convex mirror, f = +15 cm
Object distance, u = −10 cm
According to the mirror formula,
v = 6 cm
The positive value of v indicates that the image is formed behind the mirror.
The positive value of magnification indicates that the image formed is virtual
and erect. /p>
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.
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 v indicates 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.
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.
A concave lens has a negative focal length. Hence, it is a concave lens.
A convex lens has a positive focal length. Hence, it is a convex lens or a
converging lens.
1. Which of the following can make a parallel beam of light when light from a
point source is incident on it?
(a) Concave mirror as well as convex lens
(b) Convex mirror as well as concave lens
(c) Two plane mirrors placed at 90� to each other
(d) Concave mirror as well as concave lens
Ans. (a) Concave mirror as well as convex lens
Explanation: When a point source of light is at the focus of a concave mirror or
a convex lens, then emergent rays of light make a parallel beam of light. This
is the reason; concave mirror is used as reflector of headlights.
2. A 10 mm long awl pin is placed vertically in front of a concave mirror. A 5
mm long image of the awl pin is formed at 30 cm in front of the mirror. The
focal length of this mirror is
(a) � 30 cm
(b) � 20 cm
(c) � 40 cm
(d) � 60 cm
Ans. (b) � 20 cm
Explanation: object size h=10 mm, image size h�=5 mm, image distance v= -30 cm,
object
distance =?, f = ?
3. Under which of the following conditions a concave mirror can form an image
larger
than the actual object?
(a) When the object is kept at a distance equal to its radius of curvature
(b) When object is kept at a distance less than its focal length
(c) When object is placed between the focus and centre of curvature
(d) When object is kept at a distance greater than its radius of curvature
Ans. (c) When object is placed between the focus and centre of curvature
Explanation: When object is placed between F and C, an enlarged image is formed
beyond C.
4. Figure 10.1 shows a ray of light as it travels from medium A to medium B.
Refractive index of the medium B relative to medium A is
Ans. (d)
Explanation: Refractive index of medium B relative to medium A can be calculated
as follows:
nBA = Sin i / Sin r
= Sin 300/ Sin 450
= �2
5. A light ray enters from medium A to medium B as shown in Figure 10.2. The
refractive index of medium B relative to A will be
(a) greater than unity
(b) less than unity
(c) equal to unity
(d) zero
Ans. (b) less than unity
Explanation: In this case, the ray of light bends away from normal when it
enters from medium A into medium B. This shows that medium B is optically rarer
than medium A. Hence, speed of light in medium B is more than that in medium A.
So, ratio of speed of light in medium A to speed of light in medium B will be
less than one.
6. Beams of light are incident through the holes A and B and emerge out of
box through the holes C and D respectively as shown in the Figure10.3. Which of
the following could be inside the box?
(a) A rectangular glass slab
(b) A convex lens
(c) A concave lens
(d) A prism
Ans. (d) A prism
Explanation: In this case, incident rays fall perpendicularly on the point of
incidence.
Had it been a glass slab, no refraction would have taken place and rays would
have emerged in the same line as incident rays. In case of convex lens, two
parallel rays would have converged at a point. In case of concave lens, two
parallel rays would have diverged. Hence, it is a prism.
7. A beam of light is incident through the holes on side A and emerges out of
the holes on the other face of the box as shown in the Figure 10.4. Which of the
following could be inside the box?
(a) Concave lens
(b) Rectangular glass slab
(c) Prism
(d) Convex lens
Ans. (a) Concave lens
Explanation: The incident rays are parallel and emergent rays are diverging.
Hence, it is a concave lens (diverging lens).
8. Which of the following statements is true?
(a) A convex lens has 4 dioptre power having a focal length 0.25 m
(b) A convex lens has �4 dioptre power having a focal length 0.25 m
(c) A concave lens has 4 dioptre power having a focal length 0.25 m
(d) A concave lens has �4 dioptre power having a focal length 0.25 m
Ans. (a) A convex lens has 4 dioptre power having a focal length 0.25m
Explanation: The positive sign with the focal length indicates that it is a
convex lens.
9. Magnification produced by a rear view mirror fitted in vehicles
(a) is less than one
(b) is more than one
(c) is equal to one
(d) can be more than or less than one depending upon the position of the object
in front of it
Ans. (a) is less than one
Explanation: Convex mirror is used in rear view mirrors. Convex mirror always
makes smaller images. Hence, magnification produced by rear view mirror is less
than one.
10. Rays from Sun converge at a point 15 cm in front of a concave mirror. Where
should an object be placed so that size of its image is equal to the size of the
object?
(a) 15 cm in front of the mirror
(b) 30 cm in front of the mirror
(c) between 15 cm and 30 cm in front of the mirror
(d) more than 30 cm in front of the mirror
Ans. (b) 30 cm in front of the mirror
Explanation: In this case, f=-15 cm and hence c= -30cm; because radius of
curvature is double the focal length. When and object is placed on C, its image
is of the same size, inverted and is formed on C
11. A full length image of a distant tall building can definitely be seen by
using
(a) a concave mirror
(b) a convex mirror
(c) a plane mirror
(d) both concave as well as plane mirror
Ans. (b) a convex mirror
Explanation: Field of view of a convex mirror is more than any other type of
mirror. Hence, a full length image of a distant tall building can definitely be
seen by using this.
12. In torches, search lights and headlights of vehicles the bulb is placed
(a) between the pole and the focus of the reflector
(b) very near to the focus of the reflector
(c) between the focus and centre of curvature of the reflector
(d) at the centre of curvature of the reflector
Ans. (a) between the pole and the focus of the reflector
Explanation: Reflectors of headlights and searchlights are in the shape of
concave mirror. When source of light is placed at the focus, the reflected
light appears like a beam of light
13. The laws of reflection hold good for
(a) plane mirror only
(b) concave mirror only
(c) convex mirror only
(d) all mirrors irrespective of their shape
Ans. (d) all mirrors irrespective of their shape
14. The path of a ray of light coming from air passing through a rectangular
glass slab traced by four students are shown as A, B, C and D in Figure 10.5.
Which one of them is correct?
(a) A
(b) B
(c) C
(d) D
Ans. (b) B
Explanation: When ray of light enters into glass from air, it bends towards the
normal. When ray of light from glass emerges into air, it bends away from
normal. This is correctly shown by figure B.
15. You are given water, mustard oil, glycerine and kerosene. In which of
these media a ray of light incident obliquely at same angle would bend the most?
(a) Kerosene
(b) Water
(c) Mustard oil
(d) Glycerine
Ans. (d) Glycerine
Explanation: Refractive index of water is 1.33, that of kerosene is 1.44, that
of mustard oil is 1.46 and that of glycerine is 1.47.
16. Which of the following ray diagrams is correct for the ray of light
incident on a concave mirror as shown in Figure 10.6?
(a) Fig. A
(b) Fig. B
(c) Fig. C
(d) Fig. D
Ans. (d) Fig D
Explanation: In case of concave mirror, an incident ray parallel to the
principal axis passes through F after reflection.
17. Which of the following ray diagrams is correct for the ray of light
incident on a lens shown in Fig. 10.7?
(a) Fig. A.
(b) Fig. B.
(c) Fig. C.
(d) Fig. D.
Ans. (a) Fig. A
Explanation: In convex lens, the incident ray passing through F goes parallel to
the principal axis after refraction.
18. A child is standing in front of a magic mirror. She finds the image of her
head bigger, the middle portion of her body of the same size and that of the
legs smaller.
The following is the order of combinations for the magic mirror from the top.
(a) Plane, convex and concave
(b) Convex, concave and plane
(c) Concave, plane and convex
(d) Convex, plane and concave
Ans. (c) Concave, Plane and convex
Explanation: When object is between F and P of concave mirror, an enlarged and
erect image is formed behind the mirror. So, the child is seeing her head in a
concave mirror. Plane mirror makes similar sized image as object. So, the middle
portion of her body
appears to be of same size in mirror. A convex mirror makes smaller image and
hence legs are appearing smaller in mirror.
19. In which of the following, the image of an object placed at infinity will be
highly diminished and point sized?
(a) Concave mirror only
(b) Convex mirror only
(c) Convex lens only
(d) Concave mirror, convex mirror, concave lens and convex lens
Ans. (d) Concave mirror, convex mirror, concave lens and convex lens
Explanation: In case of all of the above, when an object is at infinity, image
is highlydiminished and point sized.
When a ray of light enters from one rarer medium (say air) to another denser medium (say glass), it bends towards the normal. When the same ray of light exits from second medium into first medium, it bends away from the normal. In this case, the extent of bending of ray at opposite parallels (air-glass interface and glass-air interface) is same. Due to this, the emergent ray is parallel to incident ray.
Refractive index of one medium in relation to a second medium is given by ratio of speed of light in second medium to speed of light in first medium. If v1 is the speed of light in first medium and v2 is the speed of light in second medium, then refractive index of first medium in relation to second medium can be given as follows:
When two plane mirrors are at right angles to each other, incident ray and
reflected ray will always be parallel to each other, whatever may be the angle
of incidence. Let us use following figure to understand this.
ED and DC are two plane mirrors placed at right angles to each other. An is
incident ray on CD and MN is normal at point of incidence. NQ is reflected ray
from N and is incident
on point Q.
QB is reflected ray and PQ is normal to ED.
∟ ANM =∟ MNQ
(angle i=angle r)
Since corresponding angles are equal
Hence, BQ ‖ AN proved
This means that incident ray and reflected ray will always be parallel;
irrespective of
value of angle of incidence
The following figure shows a ray of light incident obliquely. Every medium has a critical angle. When angle of incidence is more than critical angle, the ray of light comes back in the same medium. This phenomenon is called total internal reflection.
Ans. Laws of reflection are as follows:
(a) The incident ray, the refracted ray and normal at the point of incidence; all lie in the same plane.
(b) The ratio of sine of incidence to sine of refraction is a constant, for the light of a given colour and for a given pair of media. This law is also called Snell’s Law.
• ABCD is a glass slab. EF is incident ray which is incident on point O on air-glass interface.
• NO is normal and ∠ EON = ∠ i ; which is angle of incidence.
• N’O’ is normal extended towards the glass slab
and 1 ∠ = ∠ N OO r ' ; which is angle of refraction.
• OO’ is refracted ray from surface AB. It behaves like incident ray on surface CD.
• MO’ and O’M’ are normal on surface CD.
• GH is the emergent ray.
• ∠ OO M = ∠ i2 ' ; which is angle of incidence at surface CD.
• ∠ MO H = ∠ r2 ' ; which is angle of refraction at surface CD.
• It is observed that EF, NO and OO’ lie in the same plane; which is in accordance to the first law of refraction.
• It is also observed that EF ǁ GH ; which means emergent ray is parallel to incident ray.
This happens because the degree of bend at opposite surfaces of glass slab is same.
Magnification is 3 times and image distance v=80 cm
Since, object distance is taken as negative; as per sign convention so,
or, u = - 80 / 3 cm
Nature of image: Since image is formed on the other side of lens hence it is a real image and inverted image.
Nature of Lens: Enlarged image is formed by convex lens and not by concave lens, so it is a convex lens.
. The degree of divergence or convergence achieved by a given lens is called power of the lens. The unit of power of lens is diopter and is expressed by D. Focal length of lens used by first student is in positive hence it is a convex lens. The lens of second student is a concave lens.
Power of lens (first student) =+2
Power of lens (second student) =-2
