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Reflection of Light 1
When a ray of light after incidenting on a boundary separating two media comes back into the
same media, then this phenomenon, is called reflection of light.
Note : After reflection velocity, wavelength and frequency of light remains same but
intensity decreases.
If light ray incident normally on a surface, after reflection it retraces the path.
Real and virtual images
If light rays, after reflection or refraction, actually meets at a point then real image is formed
and if they appears to meet virtual image is formed.
Plane Mirror.
The image formed by a plane mirror is virtual, erect, laterally inverted, equal in size that of
the object and at a distance equal to the distance of the object in front of the mirror.
∠ i = ∠ r After reflection, velocity, wave length and frequency of light remains same but intensity decreases There is a phase change of if reflection takes place from denser medium
Boundary
Reflected ray
Normal
i r
Incident ray
x x
O^ I
(Real object) (Virtual image)
O
I
(Real image) (^) (Virtual object)
Real image
(Real image)
(Virtual object)
I
O
(Virtual image)
(Real object)
(Virtual image)
O I
2 Reflection of Light
(1) Deviation : Deviation produced by a plane mirror and by two inclined plane mirrors.
Note : If two plane mirrors are inclined to each other at 90o, the emergent ray is anti-
parallel to incident ray, if it suffers one reflection from each. Whatever be the angle
to incidence.
(2) Rotation : If a plane mirror is rotated in the plane of incidence through angle , by
keeping the incident ray fixed, the reflected ray turned through an angle 2 .
(3) Images by two inclined plane mirrors : When two plane mirrors are inclined to each
other at an angle , then number of images ( n ) formed of an object which is kept between them.
(i)
^ n ; If
even integer
(ii) If
odd integer then there are two possibilities
(a) Object is placed symmetrically (b) Object is placed asymmetrically
n
n
Note : If θ = 0o^ i.e. mirrors are parallel to each other so n i.e. infinite images will be
formed.
If θ = 90 o, 1 3
n
If θ = 72 o, 1 4
n (If nothing is said object is supposed to be symmetrically
placed).
(4) Other important informations
i r
= (180 – 2 i )^ ^ = (360^ –^2 )
Final path
Original path
2
IR
RR
IR RR
/ /
Object
Object
4 Reflection of Light
Example : 2 Two vertical plane mirrors are inclined at an angle of 60o^ with each other. A ray of light
travelling horizontally is reflected first from one mirror and then from the other. The
resultant deviation is
(a) 60o^ (b) 120o^ (c) 180 o^ (d) 240o
Solution : (d) By using ( 360 2 ) 360 2 60 240 o
Example : 3 A person is in a room whose ceiling and two adjacent walls are mirrors. How many images
are formed
[AFMC 2002]
(a) 5 (b) 6 (c) 7 (d) 8
Solution : (c) The walls will act as two mirrors inclined to each other at 90o^ and so sill form 1 3
images of the person. Now these images with object (Person) will act as objects for the
ceiling mirror and so ceiling will form 4 images as shown. Therefore total number of images
formed = 3 + 4 = 7
Note : The person will see only six images of himself( , , , , , ) ' 3
' 2
'
I 1 I 2 I 3 I 1 I I
Example : 4 A ray of light makes an angle of 10o^ with the horizontal above it and strikes a plane mirror
which is inclined at an angle to the horizontal. The angle for which the reflected ray
becomes vertical is
(a) 40o^ (b) 50o^ (c) 80 o^ (d) 100o
Solution : (a) From figure
o
Example : 5 A ray of light incident on the first mirror parallel to the second and is reflected from the
second mirror parallel to first mirror. The angle between two mirrors is
(a) 30o^ (b) 60o^ (c) 75 o^ (d) 90o
Solution : (b) From geometry of figure
180 o
o
Example : 6 A point object is placed mid-way between two plane mirrors distance ' a ' apart. The plane
mirror forms an infinite number of images due to multiple reflection. The distance between
the n th order image formed in the two mirrors is
(a) na (b) 2 na (c) na /2 (d) n^2 a
Solution : (b)
I 1
I 2 I 3
O
Three images by walls
I 1
I 2 I 3
O
Four images by ceiling
10 o
IR
Vertical RR
Horizontal line Plane mirror
Reflection of Light 5
From above figure it can be proved that seperation between n th order image formed in the
two mirrors = 2 na
Example : 7 Two plane mirrors P and Q are aligned parallel to each other, as shown in the figure. A light
ray is incident at an angle of at a point just inside one end of A. The plane of incidence
coincides with the plane of the figure. The maximum number of times the ray undergoes
reflections (including the first one) before it emerges out is
(a)
d tan
l
(b)
l tan
d
(c) ld tan
(d) None of these
Solution : (a) Suppose n = Total number of reflection light ray undergoes before exist out.
x = Horizontal distance travelled by light ray in one reflection.
So nx = l also
d
x
tan
d tan
l
n
Example : 8 A plane mirror and a person are moving towards each other with same velocity v. Then the
velocity of the image is
(a) v (b) 2 v (c) 3 v (d) 4 v
Solution : (c) If mirror would be at rest, then velocity of image should be 2 v. but due to the motion of
mirror, velocity of image will be 2 v + v = 3 v.
Example : 9 A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a
deviation of 300o. The number of images observable are
(a) 10 (b) 11 (c) 12 (d) 13
Solution : (b) By using ( 360 2 ) 300 360 2
30 o. Hence number of images 1 11
A small plane mirror placed at the centre of a spherical screen of radius R. A beam of light is falling
on the mirror. If the mirror makes n revolution. per second, the speed of light on the screen after
reflection from the mirror will be
(a) 4 nR (b) 2 nR (c)
nR
(d)
nR
Solution : (a) When plane mirror rotates through an angle , the reflected ray rotates through an angle 2 . So
spot on the screen will make 2 n revolution per second
Speed of light on screen v R 2 ( 2 n ) R 4 nR
d
l
I 1 ' (^) a /2 a / a
M ' M I order image
II order image
III order image
III order image
II order image
I order image
I 3 ' I 2 ' I 1 I 2 I 3 a / 3 a /
a / 3 a / 5 a /2 5 a /
O
d
l
x
Tricky example: 1Tricky example: 1
Reflection of Light 7
(vii) Relation between f and R :
R
f ( f concare = – ve , f convex = + ve , f plane = )
(viii) Power : The converging or diverging ability of mirror
(ix) Aperture : Effective diameter of light reflecting area.
Intensity of image Area (Aperture)^2
(x) Focal plane : A plane passing from focus and perpendicular to principle
axis.
(2) Rules of image formation and sign convention :
Rule (i) Rule (ii) Rule (iii)
(3) Sign conventions :
(i) All distances are measured from the pole.
(ii) Distances measured in the direction of incident rays are taken
as positive while in the direction opposite of incident rays are taken
negative.
(iii) Distances above the principle axis are taken positive and
below the principle axis are taken negative.
Note : Same sign convention are also valid for lenses.
Use following sign while solving the problem :
Concave mirror
Convex mirror
Real image (u ≥ f) Virtual image (u< f)
Distance of object u –
Distance of image v –
Focal length f –
Height of object O +
Height of image I –
Radius of curvature R –
Magnification m –
u –
v +
f –
O +
I +
R –
m +
u –
v +
f +
O +
I +
R +
m +
F F^ F^ F^ C^ C
-^ +
Mirror or Lens^ –
Incident ray
Principle axis
8 Reflection of Light
(4) Position, size and nature of image formed by the spherical mirror
Mirror Location of the
object
Location of the
image
Magnification,
Size of the
image
Nature
Real
virtual
Erect
inverted
(a) Concave At infinity
i.e. u = ∞
At focus i.e. v = f m << 1,
diminished
Real inverted
Away from centre
of curvature ( u >
2 f )
Between f and 2 f
i.e.
f < v < 2 f
m < 1, diminished Real inverted
At centre of
curvature u = 2 f
At centre of
curvature i.e. v =
2 f
m = 1, same size as
that of the object
Real inverted
Between centre of
curvature and
focus :
F < u < 2 f
Away from the
centre of curvature
v > 2 f
m > 1, magnified Real inverted
At focus i.e. u = f At infinity i.e. v =
m = ∞, magnified Real inverted
Between pole and
focus u < f
v > u m > 1 magnified Virtual erect
(b) Convex At infinity i.e. u =
At focus i.e. , v = f m < 1, diminished Virtual erect
Anywhere between
infinity and pole
Between pole and
focus
m < 1, diminished Virtual erect
Note : In case of convex mirrors, as the object moves away from the mirror, the image
becomes smaller and moves closer to the focus.
Images formed by mirrors do not show chromatic aberration.
For convex mirror maximum image distance is it’s focal length.
In concave mirror, minimum distance between a real object and it's real image is
zero.
( i.e. when u = v = 2 f )
Mirror formula and magnification.
For a spherical mirror if u = Distance of object from pole, v = distance of image from pole, f =
Focal length, R = Radius of curvature, O = Size of object, I = size of image, m = magnification (or
linear magnification ), m s = Areal magnification, Ao = Area of object, Ai = Area of image
(1) Mirror formula :
f v u
; (use sign convention while solving the problems).
Note : Newton’s formula : If object distance ( x 1 ) and image distance ( x 2 ) are measured
from focus instead of pole then 1 2
2
f x x
C F P
P F C
10 Reflection of Light
Different graphs
Graph between
v
and
u
(a) Real image formed by
concave mirror
(b) Virtual image formed by
concave mirror
(c) Virtual image formed by
convex mirror
Graph between u and v
for real image of concave
mirror
Graph between u and m
for virtual image by
concave mirror
Graph between u and m
for virtual image by
convex mirror.
Concepts
Focal length of a mirror is independent of material of mirror, medium in which it is placed, wavelength of incident light
Divergence or Convergence power of a mirror does not change with the change in medium.
If an object is moving at a speed vo towards a spherical mirror along it’s axis then speed of image away from
mirror is i vo u f
f v.
2
(use sign convention)
When object is moved from focus to infinity at constant speed, the image will move faster in the beginning and slower later on, towards the mirror.
As every part of mirror forms a complete image, if a part of the mirror is obstructed, full image will be formed but intensity will be reduced.
Can a convex mirror form real images? yes if (distance of virtual object) u < f (focal length)
v
u
P F
C
O
I
O F C
I Real image Virtual object
m
1
f u
m
1
u
2 f
f
f 2 f
Hyperbola
Example
s
v
u
v
u
Reflection of Light 11
Example : 10 A convex mirror of focal length f forms an image which is 1/ n times the object. The distance
of the object from the mirror is
(a) ( n – 1) f (b) f
n
n
(c) f
n
n
(d) ( n + 1) f
Solution : (a) By using
f u
f
m
Here
n
m
^ , f f So,
f u
f
n
u ( n 1 ) f
Example : 11 An object 5 cm tall is placed 1 m from a concave spherical mirror which has a radius of
curvature of 20 cm. The size of the image is
(a) 0.11 cm (b) 0.50 cm (c) 0.55 cm (d) 0.60 cm
Solution : (c) By using
f u
f
O
I
Here O 5 cm , cm
R
f 10
, u 1 m 100 cm
So,
I
I = – 0.55 cm.
Example : 12 An object of length 2.5 cm is placed at a distance of 1.5 f from a concave mirror where f is the
magnitude of the focal length of the mirror. The length of the object is perpendicular to the
principle axis. The length of the image is
(a) 5 cm, erect (b) 10 cm, erect (c) 15 cm, erect (d) 5 cm,
inverted
Solution : (d) By using
f u
f
O
I
; where I =? , O = + 2.5 cm. f f , u = – 1.5 f
2. 5 f ( 1. 5 f )
I f
I 5 cm. (Negative sign indicates that image is
inverted.)
Example : 13 A convex mirror has a focal length f. A real object is placed at a distance f in front of it from
the pole produces an image at
(a) Infinity (b) f (c) f / 2 (d) 2 f
Solution : (c) By using
f v u
2
1 1 1 f
v
f v f
Example : 14 Two objects A and B when placed one after another infront of a concave mirror of focal
length 10 cm from images of same size. Size of object A is four times that of B. If object A is
placed at a distance of 50 cm from the mirror, what should be the distance of B from the
mirror
(a) 10 cm (b) 20 cm (c) 30 cm (d) 40 cm
Solution : (b) By using
A
B A
B B
A
f u
f u
O
O
I
I
f u
f
O
I
10 50
B
u
uB 20 cm.
Example : 15 A square of side 3 cm is placed at a distance of 25 cm from a concave mirror of focal length
10 cm. The centre of the square is at the axis of the mirror and the plane is normal to the
axis. The area enclosed by the image of the wire is
Reflection of Light 13
(a) Real, and will remain at C (b) Real, and located at a point between
C and
(c) Virtual and located at a point between C and O (d) Real, and located at a point between
C and O
Solution : (d)
An object is placed infront of a convex mirror at a distance of 50 cm. A plane mirror is introduced
covering the lower half of the convex mirror. If the distance between the object and plane mirror is
30 cm, it is found that there is no parallel between the images formed by two mirrors. Radius of
curvature of mirror will be
(a) 12.5 cm (b) 25 cm (c) cm
(d) 18 cm
Solution : (b) Since there is no parallel, it means that both images (By plane mirror
and convex mirror) coinciding each other.
According to property of plane mirror it will form image at a distance of 30 cm behind it. Hence for
convex mirror u = – 50 cm, v = + 10 cm
By using
f v u
f
f cm
R 2 f 25 cm.
A convergent beam of light is incident on a convex mirror so as to converge to a
distance 12 cm from the pole of the mirror. An inverted image of the same size
is formed coincident with the virtual object. What is the focal length of the mirror
(a) 24 cm (b) 12 cm (c) 6 cm (d) 3 cm
Solution : (c) Here object and image are at the same position so this position must
be centre of curvature
R = 12 cm
R
f
PPrraaccttiiccee QQuueessttiioonnss BBaassiicc LLeevveell
1. A light bulb is placed between two mirrors (plane) inclined at an angle of 60o. Number of images formed are [NCERT 1980; CPMT 1996, 97; SCRA 1994; AIIMS 1997; RPMT 1999; AIEEE 2002; Orissa JEE 2003; MP PET 2004] (a) 2 (b) 4 (c) 5 (d) 6
Tricky example: 4
A
Object
50 cm
30 cm 20 cm
10 cm
Tricky example: 5
C
Object image
O Initiall y
C Object
O Finally
Image
C
14 Reflection of Light
2. Two plane mirrors are inclined at an angle of 72 o. The number of images of a point object placed between them will be [KCET (Engg. & Med.)1999; BCECE 2003] (a) 2 (b) 3 (c) 4 (d) 5 3. To get three images of a single object, one should have two plane mirrors at an angle of [AIEEE 2003]
(a) 30 o (b) 60 o (c) 90 o (d) 120 o
4. A man of length h requires a mirror of length at least equal to, to see his own complete image [MP PET 2003]
(a) 4
h (b) 3
h (c) 2
h (d) h
5. Two plane mirrors are at 45o^ to each other. If an object is placed between them then the number of images will be [MP PMT 2003
(a) 5 (b) 9 (c) 7 (d) 8
6. An object is at a distance of 0.5 m in front of a plane mirror. Distance between the object and image is [CPMT 2002]
(a) 0.5 m (b) 1 m (c) 0.25 m (d) 1.5 m
7. A man runs towards a mirror at a speed 15 m/s. The speed of the image relative to the man is [RPMT 1999; Kerala PET 2002]
(a) 15 ms ^1 (b) 30 ms ^1 (c) 35 ms ^1 (d) 20 ms ^1
8. The light reflected by a plane mirror may form a real image [KCET (Engg. & Med.) 2002]
(a) If the rays incident on the mirror are diverging (b) If the rays incident on the mirror are converging (c) If the object is placed very close to the mirror (d) Under no circumstances
9. A man is 180 cm tall and his eyes are 10 cm below the top of his head. In order to see his entire height right from toe to head, he uses a plane mirror kept at a distance of 1 m from him. The minimum length of the plane mirror required is [MP PMT 1993; DPMT 2001] (a) 180 cm (b) 90 cm (c) 85 cm (d) 170 cm 10. A small object is placed 10 cm infront of a plane mirror. If you stand behind the object 30 cm from the object and look at its image, the distance focused for your eye will be (a) 60 cm (b) 20 cm (c) 40 cm (d) 80 cm 11. Two plane mirrors are at right angles to each other. A man stands between them and combs his hair with his right hand. In how many of the images will he be seen using his right hand (a) None (b) 1 (c) 2 (d) 3 12. A man runs towards mirror at a speed of 15 m / s. What is the speed of his image [CBSE PMT 2000]
(a) 7.5 m / s (b) 15 m / s (c) 30 m / s (d) 45 m / s
13. A ray of light is incidenting normally on a plane mirror. The angle of reflection will be [MP PET 2000]
(a) 0 o^ (b) 90 o^ (c) Will not be reflected (d) None of these
14. A plane mirror produces a magnification of [MP PMT/PET 1997]
(a) – 1 (b) + 1 (c) Zero (d) Between 0 and +
15. When a plane mirror is rotated through an angle , then the reflected ray turns through the angle 2 , then the size of the image [MP PAT 1996]
(a) Is doubled (b) Is halved (c) Remains the same (d) Becomes infinite
16. What should be the angle between two plane mirrors so that whatever be the angle of incidence, the incident ray and the reflected ray from the two mirrors be parallel to each other (a) 60 o^ (b) 90 o^ (c) 120 o^ (d) 175 o 17. Ray optics is valid, when characteristic dimensions are [CBSE PMT 1994]
(a) Of the same order as the wavelength of light (b) Much smaller than the wavelength of light (c) Of the order of one millimeter (d) Much larger than the wavelength of light
18. It is desired to photograph the image of an object placed at a distance of 3 m from the plane mirror. The camera which is at a distance of 4.5 m from the mirror should be focussed for a distance of (a) 3 m (b) 4.5 m (c) 6 m (d) 7.5 m
16 Reflection of Light
(d) 2 mm, 18 mm, 58 mm
27. A plane mirror is placed at the bottom of the tank containing a liquid of refractive index . P is a small object at a
height h above the mirror. An observer O- vertically above P outside the liquid see P and its image in the mirror. The apparent distance between these two will be
(a) 2 h (b)
2 h
(c) 1
h (d)
h 1
28. One side of a glass slab is silvered as shown. A ray of light is incident on the other side at angle of incidence o i 45. Refractive index of glass is given as 1.5. The deviation of the ray of light from its initial path when it comes out of the slab is
(a) 90 o
(b) 180 o
(c) 120 o
(d) 45 o
29. If an object moves towards a plane mirror with a speed v at an angle to the perpendicular to the plane of the
mirror, find the relative velocity between the object and the image
(a) v
(b) 2 v
(c) 2 v cos
(d) 2 v sin
30. Figure shows a cubical room ABCD will the wall CD as a plane mirror. Each side of the room is 3 m. We place a camera at the midpoint of the wall AB. At what distance should the camera be focussed to photograph an object placed at A (a) 1.5 m (b) 3 m
(c) 6 m (d) More than 6 m
31. A man having height 6 m , want to see full height in mirror. They observe image of 2 m height erect, then used mirror is [J & K CET 2004] (a) Concave (b) Convex (c) Plane (d) None of these 32. An object of length 6 cm is placed on the principal axis of a concave mirror of focal length f at a distance of 4 f. The length of the image will be [MP PET 2003] (a) 2 cm (b) 12 cm (c) 4 cm (d) 1.2 cm 33. Convergence of concave mirror can be decreased by dipping in [AFMC 2003]
(a) Water (b) Oil (c) Both (d) None of these
34. In an experiment of find the focal length of a concave mirror a graph is drawn between the magnitudes of u and v. The graph looks like
(a) (b) (c) (d)
BBaassiicc LLeevveell
Reflection of light at spherical surface
v
u
v
u
v
u
v
u
A B
D C
3 m
O
P h
45 o
= 1.
O I
y
vO
vI
x
Reflection of Light 17
35. An object 2.5 cm high is placed at a distance of 10 cm from a concave mirror of radius of curvature 30 cm The size of the image is [BVP 2003] (a) 9.2 cm (b) 10.5 cm (c) 5.6 cm (d) 7.5 cm 36. A diminished virtual image can be formed only in [MP PMT 2002]
(a) Plane mirror (b) A concave mirror (c) A convex mirror (d) Concave- parabolic mirror
37. A point object is placed at a distance of 30 cm from a convex mirror of focal length 30 cm. The image will form at [JIPMER 2002]
(a) Infinity (b) Focus (c) Pole (d) 15 cm behind the mirror
38. The focal length of a convex mirror is 20 cm its radius of curvature will be [MP PMT 2001]
(a) 10 cm (b) 20 cm (c) 30 cm (d) 40 cm
39. A concave mirror of focal length 15 cm forms an image having twice the linear dimensions of the object. The position of the object when the image is virtual will be (a) 22.5 cm (b) 7.5 cm (c) 30 cm (d) 45 cm 40. Under which of the following conditions will a convex mirror of focal length f produce an image that is erect, diminished and virtual [AMU (Engg.) 2001] (a) Only when 2 f > u > f (b) Only when u = f (c) Only when u < f (d) Always 41. A concave mirror gives an image three times as large as the object placed at a distance of 20 cm from it. For the image to be real, the focal length should be [SCRA 1998; JIPMER 2 (a) 10 cm (b) 15 cm (c) 20 cm (d) 30 cm 42. A point object is placed at a distance of 10 cm and its real image is formed at a distance of 20 cm from a concave mirror. If the object is moved by 0.1 cm towards the mirror, the image will shift by about (a) 0.4 cm away from the mirror (b) 0.4 cm towards the mirror (c) 0.8 cm away from the mirror (d) 0.8 cm towards the mirror 43. The minimum distance between the object and its real image for concave mirror is [RPMT 1999]
(a) f (b) 2 f (c) 4f (d) Zero
44. An object is placed at 20 cm from a convex mirror of focal length 10 cm. The image formed by the mirror is [JIPMER 1999]
(a) Real and at 20 cm from the mirror (b) Virtual and at 20 cm from the mirror (c) Virtual and at 20/3 cm from the mirror (d) Real and at 20/3 cm from the mirror
45. An object is placed 40 cm from a concave mirror of focal length 20 cm. The image formed is [MP PET 1986; MP PMT/PET 199
(a) Real, inverted and same in size (b) Real, inverted and smaller (c) Virtual, erect and larger (d) Virtual, erect and smaller
46. Match List I with List II and select the correct answer using the codes given below the lists [SCRA 1998]
List I List II (Position of the object) (Magnification) (I) An object is placed at focus before a convex mirror (A) Magnification is – (II) An object is placed at centre of curvature before a concave mirror (B) Magnification is 0. (III) An object is placed at focus before a concave mirror (C) Magnification is + 1 (IV) An object is placed at centre of curvature before a convex mirror (D) Magnification is – 1 (E) Magnification is 0. Codes : (a) I-B, II-D, III-A, IV-E (b) I-A, II-D, III-C, IV-B (c) I-C, II-B, III-A, IV-E (d) I-B, II-E, III-D, IV-C
47. In a concave mirror experiment, an object is placed at a distance x 1 from the focus and the image is formed at a
distance x 2 from the focus. The focal length of the mirror would be
(a) x 1 x 2 (b) x 1 x 2 (c) 2
x^1^^ x^2 (d) 2
1 x
x
48. Which of the following forms a virtual and erect image for all positions of the object [IIT-JEE 1996]
(a) Convex lens (b) Concave lens (c) Convex mirror (d) Concave mirror
49. A convex mirror has a focal length f. A real object is placed at a distance f in front of it from the pole produces an image at [MP PAT 1996]
Reflection of Light 19
64. A short linear object of length l lies along the axis of a concave mirror of focal length f at a distance u form the pole of the mirror. The size of the image is approximately equal to [IIT 1988; BHU 2003]
(a)
1 / 2
f
u f l (b)
2
f
u f l (c)
1 / 2
u f
f l (d)
2
u f
f l
65. A point object is moving on the principal axis of a concave mirror of focal length 24 cm towards the mirror. When it is at a distance of 60 cm from the mirror, its velocity is 9 cm / sec. What is the velocity of the image at that instant (a) 5 cm/sec towards the mirror (b) 4 cm/sec towards the mirror (c) 4 cm/sec away from the mirror (d) 9 cm/sec away from the mirror 66. A convex mirror of focal length 10 cm forms an image which is half of the size of the object. The distance of the object from the mirror is (a) 10 cm (b) 20 cm (c) 5 cm (d) 15 cm 67. A concave mirror is used to focus the image of a flower on a nearby well 120 cm from the flower. If a lateral magnification of 16 is desired, the distance of the flower from the mirror should be (a) 8 cm (b) 12 cm (c) 80 cm (d) 120 cm 68. A thin rod of 5 cm length is kept along the axis of a concave mirror of 10 cm focal length such that its image is real and magnified and one end touches the rod. Its magnification will be (a) 1 (b) 2 (c) 3 (d) 4 69. A luminous object is placed 20 cm from surface of a convex mirror and a plane mirror is set so that virtual images formed in two mirrors coincide. If plane mirror is at a distance of 12 cm from object, then focal length of convex mirror, is (a) 5 cm (b) 10 cm (c) 20 cm (d) 40 cm 70. A rear mirror of a vehicle is cylindrical having radius of curvature 10 cm. The length of arc of curved surface is also 10 cm. If the eye of driver is assumed to be at large distance, from the mirror, then the field of view in radian is (a) 0.5 (b) 1 (c) 2 (d) 4 71. A vehicle has a driving mirror of focal length 30 cm. Another vehicle of dimension 2 4 1. 75 m^3 is 9 m away
from the mirror of first vehicle. Position of the second vehicle as seen in the mirror of first vehicle is
(a) 30 cm (b) 60 cm (c) 90 cm (d) 9 cm
72. A cube of side 2 m is placed in front of a concave mirror focal length 1 m with its face P at a distance of 3 m and
face Q at a distance of 5 m from the mirror. The distance between the images of face P and Q and height of images of P and Q are (a) 1 m, 0.5 m, 0.25 m (b) 0.5 m, 1 m, 0.25 m (c) 0.5 m, 0.25 m, 1 m (d) 0.25 m, 1 m, 0.5 m
73. A concave mirror of radius of curvature 60 cm is placed at the bottom of tank containing water upto a height of 20
cm. The mirror faces upwards with its axis vertical. Solar light falls normally on the surface of water and the image
of the sun is formed. If 3
(^) a^ w^ then with the observer in air, the distance of the image from the surface of water
is (a) 30 cm (b) 10 cm (c) 7.5 cm above (d) 7.5 cm below
74. A concave mirror forms an image of the sun at a distance of 12 cm from it
(a) The radius of curvature of this mirror is 6 cm (b) To use it as a shaving mirror, it must be held at a distance of 8-10 cm from the face (c) If an object is kept at a distance of 12 cm from it, the image formed will be of the same size as the object (d) All the above a alternatives are correct
9 m
2 m 2 m
Q P
3 m
20 Reflection of Light
75. A small piece of wire bent into an L shape with upright and horizontal portions of equal lengths, is placed with the horizontal portion along the axis of the concave mirror whose radius of curvature is 10 cm. If the bend is 20 cm from the pole of the mirror, then the ratio of the lengths of the images of the upright and horizontal portions of the wire is (a) 1 : 2 (b) 3 : 1 (c) 1 : 3 (d) 2 : 1 76. As the position of an object ( u ) reflected from a concave mirror is varied, the position of the image ( v ) also varies.
By letting the u changes from 0 to the graph between v versus u will be
77.
(a) b c d
78. A concave mirror has a focal length 20 cm. The distance between the two positions of the object for which the image size is double of the object size is (a) 20 cm (b) 40 cm (c) 30 cm (d) 60 cm 79. A concave mirror of focal length 10 cm and a convex mirror of focal length 15 cm are placed facing each other 40 cm apart. A point object is placed between the mirrors, on their common axis and 15 cm from the concave mirror. Find the position and nature of the image produced by the successive reflections, first at concave mirror and then at convex mirror (a) 2 cm (b) 4 cm (c) 6 cm (d) 8 cm
A nswer Sheet
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 c c c c c b b b b c b b a b c b d d c b 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 d a b b c c b a c d b a d c d c d d b d 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 b a d c a a b b, c c d d a b b d c b b d b 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 a c b d c a a a a b a d c b b a a c
v
u
v
u
v
u
v
u
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