2. reflection (solved example + exercise)

REFLECTION 16
SOLVED EXAMPLES
Ex1. Find the minimum height of a mirror required
to see the complete wall behind him.
Sol. From, OA A´ M& ME E´ we have
d
2
M
'
A
=
d
'
ME
 A´ M = 2 ME'
Again From,  EE´ M´ &  M´ B´ B
we have.
d
'
M
'
E
=
d
2
'
B
'
M
 M' B' = 2 E´ M´
Now, M M´ = A´ B´ – A´ M – M´ B´
= AB – 2 (ME´ + E´ M´ )
= AB – 2 M M´
M M´ =
3
1
AB
Thus , minimum height of the mirror be 1/3
of the wall and the person must be in the
middle of the mirror and the wall.
Ex2. Two mirrors are inclined at an angle of 50º.
Then what is the number of images formed
for an object placed in between the mirrors ?
Sol. For the given  = 50º,
50
360
360
n 

 = 7.2
The integer value of (7.2) is 7. Thus number
of images formed is 7.
Ex.3 Two plane mirrors are inclined at an angle .
A ray of light is incident on one mirror at an
angle of incidence i. The ray is reflected from
this mirror, falls on the second mirror from
where it is reflected parallel to the first
mirror. What is the value of i, the angle of
incidence in terms of  ?
90º-i
N1
N2
M2
B
O
C





X
A M1
i
i
Sol. The situation is illustrated in figure. XA is the
incident ray. BC is the final reflected ray. It is
given that BC is parallel to mirror M1. Look
at the assignment of the angles carefully.
Now N2 is normal to mirror M2. Therefore
 = 
Then from  OAB
 +  + 90º  i = 180º
or  +  + 90º  i = 180º
or i = 2  90º
Thus if the angle of incidence is i = 2  90º,
then the final reflected ray will be parallel to
the first mirror.
Ex.4 Two plane mirrors are inclined at an angle of
30º. Then the first four images of an object O
placed between the two mirrors are correctly
represented by
(A)
I1
M2
M1
I2
I3
I4
O
(B)
I2
I1
I4
I3
O
M1
M2

REFLECTION 17
(C)
I2
I1
I3
I4
O
M1
M2
(D)
I2
I1 I3
I4
O
M1
M2
Sol. The image of object O from mirror M1 is I1
and the image of I1 (the virtual object) from
mirror M2 is I3. The image of object O from
mirror M2 is I2 and the image of I2 (the virtual
object) from mirror M1 is I4. Notice that this
interpretation, according to ray diagram rules,
is valid only for Fig. (A). All others are
inconsistent. Hence correct is (A)
Ex.5 Two plane mirrors are placed at an angle  so
that a ray parallel to one mirror gets reflected
parallel to the second mirror after two
consecutive reflections. The value of  will be
(A) 30º (B) 60º
(C) 75º (D) 90º
Sol. As shown in figure, ray AB goes to mirror
M1, gets reflected and travels along BC and
then gets reflected by M2 and goes in CD
direction. If the angle between M1 and M2 be
, then
M1
B
O C
M2
A
E
D
  


In  OBC , OBC and OCB are equal to 
 3 = 180º
 = 60º
Hence correct answer is (B).
Ex.6 A girl stands at a distance 30 cm from the
mirror. She is able to see her erect image but
of 1/5 height of actual height. The mirror will
be :
(A) plane mirror
(B) concave mirror
(C) convex mirror
(D) plane convex mirror
Sol. Small and erect image is formed only by
convex mirror. Plane mirror from images
equal to object and concave mirror form
images bigger than object.
Hence correct answer is (C).
Ex.7 An object is placed at a distance of 50 cm
from a convex mirror. A plane mirror is
placed in front of the convex mirror in such a
way that it convers half of the convex mirror.
If the distance between object and plane
mirror is 30 cm then there is no parallax
between the images formed by two mirrors ,
the radius of curvature of convex mirror will
be :
50 cm
30 cm
(A) 50 cm (B) 25 cm
(C) 12.5 cm (D) 100cm
Sol. The image will be formed by the plane mirror
at a 30 cm behind it, while the image by
convex mirror will be formed at 10 cm behind
the convex mirror. Since for convex mirror
u = 50 cm as shown in figure.
v = 10 cm
50
4
50
5
1
10
50
1
f
1








5
.
12
4
50
f 
 cm
Therefore the radius of curvature of convex
mirror is
r = 2 f = 25 cm
Hence correct answer is (B).
Ex.8 There is a convex mirror of radius 50 cm. The
image of a point at a distance 50cm from the
pole of mirror on its axis will be formed at :
50 cm 50 cm
C
O

REFLECTION 18
(A) infinity
(B) pole
(C) focus
(D) 16 cm behind the mirror
Sol. u =  50 cm , f ' = 25cm
v
1
50
1
25
1



50
1
25
1
v
1


=
50
3
50
1
2


3
.
15
3
50
v 
 cm
Hence correct answer is (D)
Ex.9 A particle is moving at a constant speed v
from a large distance towards a concave
mirror of radius R along its principle axis.
Find the speed of the image formed by the
mirror as a function of the distance x of the
particles from the mirror.
V
P F C
Sol.
Let initially, the particle is at A. where,
PA = u1 = x and after one second , the
particle is at B where, PB = u2 = x – v ×1
We know,
R
u
2
uR
v
R
2
u
1
v
1





dt
du
.
)
R
u
2
(
2
.
uR
R
).
R
u
2
(
dt
dv
2




=
dt
du
.
R
u
2
R
2







For concave mirror R = (+ ve), u = (+ ve). As
the object approaches the mirror
)
ve
(
dt
du

  
   Velocity of Image U
.
R
u
2
R
dt
dv
2








Ex.10 A short linear object of length b lies along the
axis of a concave mirror of focal length f at a
distance u from the pole of the mirror. Find
the approximate size of the image.
Sol. Here, u1 is the distance of front side of the
object from the pole and u2 is that for back
side of the object.
u1 b
u2
1 2
We know,
v
1
+
u
1
=
f
1
v =
f
u
uf

 v1 =
f
u
f
u
1
1

& v2 =
f
u
f
u
2
2

It is given that u2 – u1 = b
 v2 –v1 =
f
u
f
u
2
2

–
f
u
f
u
1
1

= f 







 f
u
u
f
u
u
1
1
2
2
=
)
f
u
)(
f
u
(
)
f
u
u
u
f
u
u
u
(
f
1
2
1
2
1
2
2
1





=
)
f
u
)(
f
u
(
)
u
u
(
f
1
2
2
1
2



=
)
f
u
)(
f
b
u
(
b
f
1
1
2




As, u1 = u >> b we have
|v2 – v1| = 2
2
)
f
u
(
b
f

= b
2
f
u
f








REFLECTION 19
LEVEL # 1
Questions
based on
Properties of reflection
Q.1 When light is reflected from a mirror a
change occurs in its -
(A) phase, (B) frequency,
(C) wavelength, (D) speed
Q.2 On reflection from a plane surface, the
following gets changed –
(A) wavelength (B) frequency
(C) speed (D) amplitude
Q.3 A wave or a pulse is reflected normally from
the surface of a denser medium back into the
rarer medium. The phase change caused by
the reflection -
(A) 0 (B) /2
(C)  (D) 3/2
Q.4 The frequency of incident ray is 3 × 108 Hz.
The frequency after reflection -
(A) decreases (B) remain same
(C) increases (D) either 1 or 3
Q.5 The images of clouds and trees in water
always less bright than in reality –
(A) because water is forming the image dirty
(B) because there is an optical illusion
due to which the image appears to be less
bright
(C) because only a portion of the incident
light is reflected and quite a large portion
goes mid water
(D) because air above the surface of water
contains a lot of moisture
Laws of reflection
Questions
based on
Q.6 If a ray of light is incident on a plane mirror
at an angle of incidence of 30º, then deviation
produced by mirror is -
(A) 30º (B) 60º
(C) 90º (D) 120º
Q.7 A rays is incident at an angle 38º on a mirror.
The angle between normaland reflected rayis -
(A) 38º (B) 52º
(C) 90º (D) 76º
Image formation by plane mirror
Questions
based on
Q.8 The image of a real object formed by a plane
mirror is -
(A) Erect, real and of equal size
(B) Erect, virtual and of equal size
(C) Inverted, real and of equal size
(D) Inverted, virtual and of equal size
Q.9 If you want to see your full image, then
minimum size of the mirror -
(A) should be of your height
(B) should be half of your height
(C) should be twice of your height
(D) depends upon distance from the mirror
Q.10 Mark the correct options -
(A) If the incident rays are converging, we
have a real object.
(B) If the final rays are converging, we have a
real image.
(C) The image of a virtual object is called a
virtual image.
(D) If the image is virtual, the corresponding
object is called a virtual object.
Q.11 A point source of light is placed in front of a
plane mirror -
(A) All the reflected rays meet at a point
when produced backward.
(B) Only the reflected rays close to the
normal meet at a point when produced
backward.
(C) Only the reflected rays making a small
angle with the mirror, meet at a point
when produced backward.
(D) Light of different colours make different
images

REFLECTION 20
Q.12 Which of the following is not the case with
image formed by a plane mirror -
(A) It is erect
(B) It is virtual
(C) It is diminished
(D) It is at the same distance as the object
Q.13 A man 160 cm height stands in front of a
plane mirror. His eyes are at a height of
150 cm from the floor. Then the minimum
length of the plane mirror for him to see his
full length image is -
(A) 85 cm (B) 170 cm
(C) 80 cm (D) 340 cm
Q.14 Which of the following letters do not suffer
lateral inversion -
(A) HGA (B) HOX (C) VET (D) YUL
Q.15 A small object is 10 cm in front of a plane
mirror. A man stands 30 cm from the mirror,
behind the object and looks at the object's
image. He should focus his eyes to see the
image at a distance -
(A) 25 cm. (B) 35 cm.
(C) 45 cm. (D) 40 cm.
Q.16 A plane mirror produces a magnification of -
(A) –1 (B) + 1
(C) zero (D) between 0 and + 
Motion of image by plane mirror
Questions
based on
Q.17 An object is initially at a distance of 100 cm
from a plane mirror. If the mirror approaches
the object at a speed of 5 cm/s. Then after 6
s the distance between the object and its
image will be -
(A) 60 cm (B) 140 cm
(C) 170 cm (D) 150 cm
Q.18 A plane mirror is approaching you at 10 cm
per second. You can see your image in it. At
what speed will your image approach you -
(A) 10 cm/s (B) 5 cm/s
(C) 20 cm/s (D) 15 cm/s
Q.19 If an object approaches towards a plane
mirror with velocity Vthen image
approaches the object with velocity -
(A) V (B)1.5V
 C) 2 V (D) 3 V
Q.20 A car is moving towards a plane mirror at a
speed of 30 m/s. Then the relative speed of its
image with respect to the car will be -
(A) 30 m/s (B) 60 m/s
(C) 15 m/s (D) 45 m/s
Q.21 An object is approaching a plane mirror at
5 cms per second. A stationary observer sees
the image. At what speed will the image
approach the stationary observer -
(A) 5 cms per second
(B) 20 cms per second
(C) 10 cms per second
(D) 15 cms per second
Q.22 A person is standing in front of a plane
mirror. If the mirror recedes with velocity v,
the relative separation of person and his image
per second is -
(A) 0 (B) v (C) 2 v (D) v/2
Two inclined plane mirrors
Questions
based on
Q.23 Two mirrors are placed perpendicular to each
other. A ray strikes the first mirror and after
reflection from the first mirror it falls on the
second mirror. The ray after reflection from
second mirror will emerge -
(A) Perpendicular to the original ray
(B) Parallel to the original ray
(C) At 45° to the original ray
(D) At 60° to the original ray
Q.24 An object is placed between two plane
mirrors set at 60° to each other. The
maximum number of images seen will be -
(A) 2 (B) 3 (C) 5 (D) 6
Q.25 A person is in a room whose ceiling and two
adjacent walls are mirrors. How many images
are formed ?
(A) 5 (B) 6 (C) 7 (D) 8
Q.26 The number of images observable between
two parallel plane mirrors is -
(A) 2 (B) 4
(C) 11 (D) infinite
Q.27 An object is placed symmetrically between
the two plane mirrors inclined at an angle of
30º, then the total number of images formed,
is -
(A) 12 (B) 2
(C) 11 (D) infinite

REFLECTION 21
Q.28 If an object is placed unsymmetrically
between two plane mirrors, inclined at the
angle of 60°, then the total number of images
formed is -
(A) 5 (B) 4 (C) 2 (D) infinite
Q.29 If an object is placed unsymmetrically
between two plane mirrors, inclined at an
angle of 72°, then the total number of images
formed is -
(A) 5 (B) 4 (C) 2 (D) Infinity
Q.30 Two plane mirrors are inclined to one another
at an angle of 60º. A ray is incident on mirror
M1 at an angle i. The reflected ray from
mirror M2 is parallel to mirror M1 as shown
in figure. The angle of incidence i is -
60º
M1
M2
i
i
O
(A) 20º (B) 10º (C) 30º (D) 40º
Q.31 Images formed by an object placed between
two plane mirrors whose reflecting surfaces
make an angle of 90° with one another lie on -
(A) Straight line (B) Zig-zag curve
(C) Circle (D) Ellipse
at an angle of 40°. A point object is placed
symmetrically in between them. The number
of images formed due to reflection at both
mirrors is -
(A) Infinite (B) 9
(C) 8 (D) 6
Q.33 At what angle must two plane mirrors be
placed so that incident and resulting reflected
rays are always parallel to each other -
(A) 0° (B) 30° (C) 60° (D) 90°
Q.34 How many images of himself, does an
observer see if two adjacent walls of
rectangular room are mirror surfaced -
(A) 3 (B) 5 (C) 7 (D) 9
Q.35 A ray gets successively reflected from two
mirrors inclined at an angle of 40º. If the
angle of incidence on the first mirror is 60º,
then the net deviation of this ray is -
(A) 40º (B) 280º
(C) 80º (D) 100º
Questions
based on
Focal length of spherical mirrors
Q.36 The focal length of spherical mirror is -
(A) Maximum for red light
(B) Maximum for blue light
(C) Maximum for white light
(D) Same for all lights
Q.37 If a spherical mirror is immersed in a liquid,
its focal length will -
(A) Increase
(B) Decrease
(C) Remains unchanged
(D) Depends on the nature of liquid
Reflection from concave mirror
Questions
based on
Q.38 In a concave mirror experiment, an object is
placed at a distance x1 from the focus and the
image is formed at a distance x2 from the
focus. The focal length of the mirror would
be-
(A) x1x2 (B) 2
1x
x
(C) 2
1 x
/
x (D)
2
x
x 2
1 
Q.39 An object is placed at a distance of 40 cm in
front of a concave mirror of focal length
20cm. The image produced is -
(A) virtual and inverted
(B) real and erect
(C) real inverted and diminished
(D) real, inverted and of same size as the
object.

REFLECTION 22
Q.40 An object of length 5cm is placed at a
distance 1m from a concave mirror. If radius
of curvature of mirror is 20 cm. Size of image
will be -
(A) 0.11 cm (B) 0.50 cm
(C) 0.55 cm (D) 0.60 cm
Q.41 When an object is placed at a distance of x m
from a concave mirror, the magnification of
the real image produced is 2. Then the radius
of curvature of the mirror is -
(A) 4x (B) 4x2 (C) 4x/3 (D) 3x/4
Q.42 A short linear object is placed along optic
axis of a concave mirror. If distance of nearer
end of the object from the mirror is greater
than radius of curvature then -
(A) a real and elongated image will be
formed.
(B) a virtual and elongatedimage will be formed.
(C) a real and diminished image will be formed.
(D) a virtual anddiminishedimage will be
formed.
Q.43 Sun subtends an angle of 0.5º at the pole of a
concave mirror or radius of curvature 15 m.
The diameter of the image of the sun formed
by the mirror is -
(A) 8.55 cm (B) 7.55 cm
(C) 6.55 cm (D) 5.55 cm
Q.44 The focal length of a concave mirror is
12 cm. Where should an object of length 4 cm
be placed sothat animage 1cm longis formed ?
(A) 48 cm (B) 3 cm
(C) 60 cm (D) 15 cm
Q.45 The focal length of a concave mirror is
20 cm. Determine where an object must be
placed to form an image magnified two times
when the image is real -
(A) 30 cm from the mirror
(B) 10 cm from the mirror
(C) 20 cm from the mirror
(D) 15 cm from the mirror
Q.46 In the above question, if the magnified image
is virtual, the distance of the object from the
mirror must be -
(A) 30 cm (B) 10 cm
(C) 20 cm (D) 15 cm
Q.47 A virtual image, larger than the object can be
produced by -
(A) convex mirror (B) concave mirror
(C) plane mirror (D) concave lens
Q.48 Given a point source of light, which of the
following can produce a parallel beam of
light-
(A) convex mirror
(B) concave mirror
(C) concave lens
(D) two plane mirrors inclined at 90º to each
other
Q.49 The image formed by a concave mirror -
(A) is always real
(B) is always virtual
(C) is certainly real if the object is virtual
(D) is certainly virtual if the object is real.
Q.50 A short linear object is placed along optic
axis of a concave mirror. If the object is in
between pole and focus, then -
(A) a virtual image will be formed.
(B) a real diminished image will be formed.
(C) If object is in between pole and focus
then a real and elongated image will be
formed.
(D) none of these.
Reflection from convex mirror
Questions
based on
Q.51 The image formed by convex mirror of focal
length 30 cm is a quarter of the size of the
object. Then the distance of the object from
the mirror, is -
(A) 30 cm (B) 90 cm
(C) 120 cm (D) 60 cm
Q.52 A convex mirror is used to form an image of
a real object. Then tick the wrong statement -
(A) the image lies between the pole and the
focus
(B) the image is diminished in size
(C) the image is erect
(D) the image is real

REFLECTION 23
Q.53 The largest distance of the image from a
convex mirror of focal length 10 cm can be -
(A) 20 cm
(B) infinite
(C) 10 cm
(D) depends on the position of the object
Q.54 An object is placed at a distance of 25 cm
from the pole of a convex mirror and a plane
mirror is set so that the virtual images formed
by two mirrors do not have any parallax. The
plane mirror is 20 cm from the object. The
focal length of the mirror is -
(A) 37.5 cm (B) –7.5 cm
(C) –37.5 cm (D) + 75 cm
Q.55 The rear-view mirror of a car is -
(A) Plane
(B) Convex
(C) Concave
(D) None of the above
Q.56 An inverted image of a real object can be
seen in a convex mirror -
(A) Under no circumstances
(B) When object is very far from the mirror
(C) When the object is at a distance equal to
the radius of the mirror
(D) When the object is at a distance equal to
the focal length of the mirror
Q.57 A point source is placed 15 cm away from a
convex mirror. A virtual image is formed at a
distance of 6 cm. The radius of curvature of
the mirror is -
(A) 4.3 cm (B) 8.6 cm
(C) 10 cm (D) 20 cm
Q.58 A boy of height 1 m stands in front of a
convex mirror. His distance from the mirror is
equal to its focal length. The height of his
image is -
(A) 0.25 m (B) 0.33 m
(C) 0.5 m (D) 0.67 m
Q.59 A convex mirror has a focal length f. A real
object is placed at a distance f infront of it
from the pole, produces an image at -
(A) infinity (B) f
(C) f / 2 (D) 2 f

REFLECTION 24
LEVEL # 2
Q.1 Two parallel plane mirrors M1 and M2 have a
length of 2 m each and are 10 mm apart. A
ray of light is incident on one end of mirror
M2 at an angle of 30º. The number of
reflections light undergoes before reaching
the other end is –
(A) 346 (B) 134 (C) 80 (D) 173
Q.2 It is necessary to illuminate the bottom of a
well by reflected solar beam when the light is
incident at an angle of  = 40º to the vertical.
At what angle  to the horizontal should a
plane mirror be placed ?
(A) 70º (B) 20º (C) 50º (D) 40º
Q.3 A ray of light makes an angle of 20º with the
horizontal 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) 80º
(C) 55º & 35º (D) 100º
Q.4 Two plane mirrors parallel to each other and
an object O placed between them. Then the
distance of the first three images from the
mirror M2 will be (in cm) –
 
15 cm
cm
O
(A) 5, 10, 15 (B) 5, 15, 30
(C) 5, 25, 35 (D) 5, 15, 25
Q.5 Figure below shows two plane mirrors and an
object O placed between them. What will be
distance of the first three images from the
mirror M2
cmcm

 
(A) 2 cm, 8 cm, 14 cm
(B) 2 cm, 12 cm, 18 cm
(C) 2 cm, 18 cm, 22 cm
(D) 2cm, 24 cm, 38cm
Q.6 The mirrors are perpendicular to each other as
shown in the Fig. A light ray AB is incident
on the mirror M1. Then the reflected ray will
also suffer a reflection from the mirror M2.
Then the final ray after reflection from M2
will be parallel to the incident ray, if -
A
M2
M1
B
i
(A) i = 45º
(B) i = 60º
(C) i < 30º
(D) for any i between 0º and 90º
Q.7 In the phenomenon of reflection -
(A) velocity changes
(B) frequency changes
(C) wavelength changes
(D) phase may or may not change
Q.8 A man moves towards a plane mirror with a
velocity v in a direction making an angle 
with the normal to the mirror. The magnitude
of velocity of the image relative to man
normal to mirror will be -
(A) 2v (B) 2v cos
(C) 2v sin (D) 2v/cos
Q.9 Fig. shows a cubical room ABCD with the
wall CD as a plane mirror. Each side of the
room is 3m. We place a camera at the
midpoint of the wall AB. At what distance
should the camera be focussed to photograph
of image of an object placed at A
A B
3 m
Camera

D C
(A) 1.5 m (B) 3 m
(C) 6 m (D) 6.18 m

REFLECTION 25
Q.10 When a plane mirror is placed horizontally on
level ground at a distance of 60 metres from
the foot of a tower, the top of the tower and
its image in the mirror subtend an angle of
900 at the eye. The height of the tower is -
(A) 30 metres (B) 60 metres
(C) 90 metres (D) 120 metres
Q.11 A point object is placed midway between two
plane mirrors distance 'a' apart. The plane
mirrors form an infinite number of images
due to multiple reflections. The distance
between nth order image formed in the two
mirrors is-
(A) na (B) 2 na
(C)
2
na
(D) n2 a
Q.12 Number of images of an object kept
symmetrically between two mirrors inclined
at angle 72°, would be -
(A) two (B) three
(C) six (D) four
at an angle of 40o. A point object is placed in
between them. The number of images formed
due to reflection at both mirrors is -
(A) Infinite (B) 9
(C) 8 (D) 6
Q.14 When a clock is viewed in a mirror, the
needles exhibit a time which appears to be
8.20. Then the actual time will be -
(A) 4.40 (B) 3.40
(C) 8.20 (D) 3.20
Q.15 A ray of light making an angle 10º with the
horizontal is incident on a plane mirror
making a angle  with the horizontal. What
should be the value of  so that the reflected
ray goes vertically upwards -
(A) 20º (B) 30º
(C) 40º (D) 45º
Q.16 A mirror is inclined at an angle of º with the
horizontal. If a ray of light is incident at an
angle of incidence º then the reflected ray
makes the following angle with the
horizontal-




incident ray
(A) º (B) 2º
(C)
2
º

(D) none of these
Q.17 Two plane mirrors are inclined to each other
at an angle 60º. If a ray of light incident on
the first mirror is parallel to the second
mirror, it is reflected from the second mirror -
(A) Perpendicular to the first mirror
(B) Parallel to the first mirror
(C) Parallel to the second mirror
(D) Perpendicular to the second mirror
Q.18 Rays of light strike a horizontal plane mirror
at an angle of 45º. A second plane mirror is
arranged at an angle  with it. If the ray after
reflection from the second mirror goes
horizontally parallel to the first mirror then  is -
(A) 45º (B) 60º (C) 67.5º (D) 135º
Q.19 In case of concave mirror, the minimum
distance between a real object and its real
image is -
(A) f (B) 2f
(C) 4f (D) zero
Q.20 The magnification m, the image position v
and focal length f are related to one another
by the relation –
(A) m =
f
v
f 
(B) m =
v
f
f

(C) m = –
f
v
f 
(D) m = –
f
v
f

Q.21 The relation between magnification m, the
object position u and focal length f of the
mirror is –
(A) m =
f
u
f 
(B) m =
u
f
f

(C) m =
f
u
f 
(D) m =
u
f
f


REFLECTION 26
Q.22 A concave mirror of focal length f produces
an image n times the size of the object. It the
image is real then the distance of the object
from the mirror, is -
(A) (n – 1 ) f
(B) {(n- 1) / n } f
(C) {(n + 1 ) / n } f
(D) (n + 1 ) f
Q.23 A convex mirror of focal length f produces an
image th
n
1
of the size of the object. The
distance of the object from the mirror is -
(A) (n-1) f (B) f
n
1
n





 
(C) f
n
1
n





 
(D) ( n + 1 ) f
Q.24 The focal length of a concave mirror is f and
the distance of the object from the focus is u
(away from the mirror). The magnification
produced by the mirror is -
(A) f / u (B) uf
(C) u / f (D) f 2 / u
Q.25 At what distance from a concave mirror of
focal length 10 cm must an object be placed
in order that an image double its size may be
obtained ?
(A) 5 cm only
(B) 15 cm only
(C) either 5 cm or 15 cm
(D) at 10 cm
Q.26 A spherical mirror forms a real image of a
point object placed in front. The distance of
the image and object from the mirror is 30 cm
and 0.2 m respectively. The focal length and
nature of the mirror are -
(A) 120 mm;concave
(B) 120 mm; convex
(C) 60 cm; concave
(D) 60 cm; convex
Q.27 An object is placed at a distance u cm from a
concave mirror of focal length f cm. The real
image of the object is received on a screen
placed at a distance of v cm from the mirror.
The values of u are changed and the
corresponding values of v are measured.
Which one of the graphs shown in the figure
represents the variation of
v
1
with
u
1
?
(A)
1/v
1/u
O
(B)
1/v
1/u
O
(C)
1/v
1/u
O
(D)
1/v
1/u
O
Q.28 A convergent beam of light converges to a
point 20 cm behind the convex mirror on the
principal axis. An inverted image of the same
size is formed coincident with the virtual
object. Then, the focal length of the convex
mirror is -
(A) 20 cm (B) 10 cm
(C) 40 cm (D) 30 cm
Q.29 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
9cm/sec. What is the velocity of the image at
that instant-
(A) 5 cm/sec towards the mirror
(B) 4 cm/sec towards the mirrors
(C) 4 cm/sec away from mirror
(D) 9 cm/sec away from mirror
Q.30 Consider the following statements : if an
object is placed between a concave mirror
and its focal point, then the image formed
will be -
I. Real,
II. magnified
III. erect
of these statements :
(A) I and II are correct
(B) I and III are correct
(C) II and III are correct
(D) I, II and III are correct
Q.31 A convex mirror and a concave mirror of
radius 10 cm each are placed 15 cm apart
facing each other. An object is placed
midway between them. If the reflection first
takes place in the concave mirror and then in
convex mirror, the position of the finalimage is –
(A) on the pole of the convex mirror
(B) on the pole of the concave mirror
(C) at a distance of 10 cm from convex mirror
(D) at a distance of 5 cm from concave mirror

REFLECTION 27
LEVEL # 3
Q.1 It is desired to photograph the image of an
object placed at a distance of 3 m from a
plane mirror. The camera, which is at a
distance of 4.5 m from the mirror, should be
focused for a distance of -
(A) 3 m (B) 4.5 m (C) 6 m (D) 7.5 m
Q.2 An object is placed between two plane
mirrors inclined at an angle to each other. If
the number of images formed is 7 then the
angle of inclination is -
(A) 15º (B) 30º (C) 45º (D) 60º
Q.3 In case of three plane - mirrors meeting at a
point to form a corner of a cube, if incident
light suffers one reflection on each mirror -
(A) the emergent ray is antiparallel to
incident one
(B) The emergent ray is perpendicular to
incident one
(C) The emergent ray is in phase with
incident one
(D) the emergent ray is in opposite phase with
incident one
Q.4 Two plane mirrors are parallel to each other
and spaced 20 cm apart. An object is kept in
between them 15 cm from A. Out of the
following at which point is an image not
formed in mirror A (distances measured from
the mirror A) -
(A) 15 cm (B) 25 cm
(C) 45 cm (D) 55 cm
Q.5 A plane mirror rotating at an angular velocity
of 3 radian/s reflects a light beam. The
angular velocity of the reflected beam is -
(A) 3 rad/s (B) 6 rad/s
(C) 9 rad/s (D) 12 rad/s
Q.6 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
Q.7 In case of image formation by plane mirrors -
(A) Object can be real and image virtual
(B) Object can be virtual and image real
(C) Both object and image can be real
(D) Both object and image can be virtual
Q.8 A ray of light is incident on a mirror which is
fitted along with other mirror. Angle between
the two mirrors is . If the ray undergoes
successive reflections first at the first mirror
and then at the second mirror then final
deviation produced will be -
(A)  (B) 2 (C) /2 (D) 0
Q.9 Radius of curvature of concave mirror is 40
cm and the size of real image is twice as that
of the object. The object distance is -
(A) 20 cm (B) 30 cm (C) 60 cm (D) 40 cm
Q.10 A convex mirror of focal length f (in air) is
immersed in water 







3
4
. The focal length
of the mirror in water will be -
(A) f (B) 





3
4
f
(C) 





4
3
f (D) 





3
7
f
Q.11 If the size of a virtual image formed by a
concave mirror of focal length 15 cm is twice
the size of the object, then distance of object
from mirror is -
(A) 15 cm (B) 10 cm
(C) 7.5 cm (D) 5 cm
Q.12 An object is placed at a distance of 20 cm
from the pole of a concave mirror whose
focal length is 20 cm. Then image is formed
at -
(A) 20 cm from the pole of the mirror
(B) 40 cm from the pole of the mirror
(C) at the pole of the mirror
(D) at infinity

REFLECTION 28
Q.13 A convex mirror has a focal length of 20 cm.
A real object is placed at a distance of 20 cm
in front of the mirror from the pole. Mirror
will produce an image at -
(A) 10 cm (B) 20 cm
(C) 30 cm (D) 40 cm
Q.14 A luminous object is placed 20 cm from the
surface of a convex mirror and a plane mirror
is adjusted in such a way that virtual images
formed by two mirrors coincides. If focal
length of convex mirror is 5 cm, then distance
between plane mirror and object will be -
(A) 10 cm (B) 12 cm
(C) 15 cm (D) 17.5 cm
Q.15 A candle flame of 3 cm is placed at 300 cm
from a wall. A concave mirror is kept at
distance x from the wall in such a way that
image of the flame on the wall is 9 cm. Then x
is -
(A) 339 cm (B) 900 cm
(C) 450 cm (D) 423 cm
Q.16 Image formed by a concave mirror radius of
curvature 40 cm is half the size of the object.
Then distance of object and its image from
the mirror will be -
(A) 30 cm and 60 cm (B) 60 cm and 120 cm
(C) 60 cm and 30 cm (D) 120 cm and 60 cm
Q.17 Focal length of convex mirror fitted in a car is
20 cm. Another car 2m broad, 21.6 cm high is
6 meter away from the first car. Then position
of the second car as seen in the mirror will
be-
(A) 21.6 cm (B) 6 m
(C) 41.6 cm (D) 19.4 cm
Q.18 When an object in placed at a distance of 25
cm from a mirror, the magnification is
m1.The object is moved 15 cm away with
respect to the earlier position, magnification
becomes m2. If m1 / m2 = 4, the focal length
of the mirror is -
(A) 10 cm. (B) 30 cm.
(C) 15 cm. (D) 20 cm.
Q.19 A small piece of wire bent into on 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
Each of the questions given below consist
of Statement – I and Statement – II.
Use the following Key to choose the
appropriate answer.
(A) If both Statement- I and Statement- II
are true, and Statement - II is the
correct explanation of Statement–
I.
(B) If both Statement - I and Statement - II
are true but Statement - II is not the
correct explanation of Statement – I.
(C) If Statement - I is true but Statement -
II is false.
(D) If Statement - I is false but Statement -
II is true.
Q.20 Statement-I : A ray incident along normal to
the mirror retraces its path.
Statement-II : In reflection, angle of
incidence is always equal to angle of
reflection
Q.21 Statement I : The image formed by a convex
mirror cannot be formed on the screen.
Statement II: The image formed by convex
mirror is always virtual.
Q.22 Statement I : A concave mirror is preferred
to a plane mirror for shaving.
Statement II: When a man keeps his face
between pole and focus of a mirror an erect
and magnified virtual image is formed.
Q.23 Statement I : Focal length of a spherical
mirror depends on the distances of object and
image from the mirror.
Statement II:
u
1
v
1
f
1



REFLECTION 29
Q.24 Statement I : Magnification of a convex
mirror is always positive .
Statement II: m =
u
v

and convex mirror
always forms virtual image.
Q.25 Statement I : Light reflected from any
surface obeys the law of reflection.
Statement II: Distance measured in the
direction of light are taken as positive.
Q.26 Statement I : Convex mirror is used as a rear
view mirror.
Statement II: Convex mirror always forms
virtual, erect and diminished image for all
positions of the object.
Passage # 1
A point object is placed on the principal axis
of a concave mirror quite far away from the
pole and moved at a constant speed 0.5
cm/sec towards the pole. Its image also
moves. It is found that the object and the
image cross each other at a point which is at a
distance 50 cm from the pole.
Q.27 Focal length of the mirror is -
(A) 50 cm (B) 35 cm (C) 25 cm (D) 15 cm
Q.28 Position of the image when the object is at a
distance 30 cm from the pole is -
(A) 150 cm from the pole in front of the
reflecting surface
(B) 120 cm from the pole behind the mirror
(C) 150 cm from the pole behind the mirror
(D) 120 cm from the pole in front of the
reflecting surface
Q.29 Speed of the image when the object is
crossing the position which is at distance 30
cm from the pole is -
(A) 15 cm/sec (B) 12.5 cm/sec
(C) 9.5 cm/sec (D) 1 cm/sec
Passage # 2
An object is placed perpendicular to the
principal axis of a concave mirror at a
position (1) such that the image formed is real
with a magnification 2. The object is now
shifted to another position (2) at a distance 15
cm from the position (1) and a real image is
obtained with a magnification 8. Shifting the
position of object from (2) to a third position
(3) gives an image with magnification
2
1
.
Q.30 Position (1) of the object is between -
(A) centre of curvature and 
(B) focus and centre of curvature
(C) pole and focus
(D) pole and centre of curvature
Q.31 Position of the image when the object is at
position (2) is -
(A) between centre of curvature and 
(B) between focus and centre of curvature
(C) between pole and focus
(D) at centre of curvature
Q.32 Position of the image when the object is at
position (3) is -
(A) between centre of curvature and 
(B) between focus and centre of curvature
(C) at focus
(D) between pole and focus
Q.33 Distance of position (1) of the object from
pole and that of position (2) of object from
pole are, respectively -
(A) 60 cm, 75 cm (B) 75 cm, 60 cm
(C) 60 cm, 45 cm (D) 45 cm, 30 cm
Q.34 Focal length of the mirror is -
(A) – 60 cm (B) – 40 cm
(C) – 30 cm (D) – 25 cm
Q.35 Match the column :
Column I Column II
(A) Concave-mirror, u < f (P) Virtual,
diminished
image
(B) Convex mirror, u > f (Q) Real,
diminished image
(C) Concave mirror, (R) Virtual,
enlarged
f < u < 2f image
(D) Concave mirror, (S) Real, enlarged
u > 2f image

REFLECTION 30
ANSWER KEY
LEVEL # 1
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. A D C B C D A B B B A C C B D B B C C B
Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Ans. A C B C C D C A A C C C D A B D C B D C
Q.No. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
Ans. C C C C A B B B C A B D C A B A D C C
LEVEL # 2
Q.No. 1 2 3 4 5 6 7 8 9 10
Ans. A A C C C D D B D B
Q.No. 11 12 13 14 15 16 17 18 19 20
Ans. B D C B C D B C D A
Q.No. 21 22 23 24 25 26 27 28 29 30
Ans. B C A A C A C B C C
Q.No. 31
Ans. A
LEVEL # 3
Q.No. 1 2 3 4 5 6 7 8 9 10
Ans. D C A,D C B B A,B B B A
Q.No. 11 12 13 14 15 16 17 18 19 20
Ans. C D A B C C D D B A
Q.No. 21 22 23 24 25 26 27 28 29 30
Ans. A A D A B A C A B B
Q.No. 31 32 33 34
Ans. A B C B A  R, B  P, C  S, D  Q
35

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