DC Pandey Solutions (JEE Advance): Reflection of Light | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


For JEE Advanced 
Objective Questions 
  Single Option Correct 
Q 1.  An insect of negligible mass is sitting on a block of mass M, tied with a spring of force constant k. 
The block performs simple harmonic motion with amplitude A in front of a plane mirror placed as 
shown. The maximum speed of insect relative to its image will be 
 
 (a) 
k
A
M
   (b) 
A 3 k
2M
  (c) 
k
A3
M
   (d) 
M
2A
k
 
Q 2.  A plane mirror is falling vertically as shown in the figure. If S is a point source of light, the rate of 
increase of the length AB is 
 
  (a) directly proportional to x   (b) constant but not zero 
  (c) inversely proportional to x  (d) zero 
Q 3.  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 
Q 4.  Two plane mirrors L
1
 and L
2
 are parallel to each other and 3 m apart. A person standing x m from 
the right mirror L
2
 looks into this mirror and sees a series of images. The distance between the first 
and second image is 4 m. Then the value of x is 
 
  (a) 2 m   (b) 1.5 m  (c) 1 m   (d) 2.5 m 
Q 5.  A piece of wire bent into an L shape with upright and horizontal portion of equal lengths 10 cm 
each is placed with the horizontal portion along the axis of the concave mirror towards pole of 
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 portion of the wire is 
  (a) 1 :2   (b) 1:3    (c) 1:1    (d) 2 : 1 
Q 6.  A point object at 15 cm from a concave mirror of radius of curvature 20 cm is made to oscillate 
along the principal axis with amplitude 2 mm. The amplitude of its image will be 
Page 2


For JEE Advanced 
Objective Questions 
  Single Option Correct 
Q 1.  An insect of negligible mass is sitting on a block of mass M, tied with a spring of force constant k. 
The block performs simple harmonic motion with amplitude A in front of a plane mirror placed as 
shown. The maximum speed of insect relative to its image will be 
 
 (a) 
k
A
M
   (b) 
A 3 k
2M
  (c) 
k
A3
M
   (d) 
M
2A
k
 
Q 2.  A plane mirror is falling vertically as shown in the figure. If S is a point source of light, the rate of 
increase of the length AB is 
 
  (a) directly proportional to x   (b) constant but not zero 
  (c) inversely proportional to x  (d) zero 
Q 3.  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 
Q 4.  Two plane mirrors L
1
 and L
2
 are parallel to each other and 3 m apart. A person standing x m from 
the right mirror L
2
 looks into this mirror and sees a series of images. The distance between the first 
and second image is 4 m. Then the value of x is 
 
  (a) 2 m   (b) 1.5 m  (c) 1 m   (d) 2.5 m 
Q 5.  A piece of wire bent into an L shape with upright and horizontal portion of equal lengths 10 cm 
each is placed with the horizontal portion along the axis of the concave mirror towards pole of 
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 portion of the wire is 
  (a) 1 :2   (b) 1:3    (c) 1:1    (d) 2 : 1 
Q 6.  A point object at 15 cm from a concave mirror of radius of curvature 20 cm is made to oscillate 
along the principal axis with amplitude 2 mm. The amplitude of its image will be 
  (a) 2 mm   (b) 4 mm   (c) 8 mm   (d) None of these 
Q 7.  A ray of light falls on a plane mirror. When the mirror is turned, about an axis at right angles to 
the plane of mirror by 20° the angle between the incident ray and new reflected ray is 45°. The 
angle between the incident ray and original reflected ray was therefore 
  (a) 35° or 50°   (b) 25° or 65°  (c) 45° or 5°   (d) None of these 
Q 8.  A person AB of height 170 cm is standing in front of a plane mirror. His eyes are at height 164 
cm. At what distance from P should a hole be made in mirror so that he cannot see his hair 
 
  (a) 167 cm   (b) 161 cm  (c) 163 cm   (d) 165 cm 
Q 9.  Two blocks each of masses m lie on a smooth table. They are attached to two other masses as 
shown in figure. The pulleys and strings are light. An object O is kept at rest on the table. The 
sides AB and CD of the two blocks are made reflecting. The acceleration of two images formed in 
those two reflecting
 
surfaces with respect to each other is 
 
 (a) 
5g
6
   (b) 
5g
3
   (c) 
17g
12
   (d) 
17g
6
 
Q 10. Two plane mirrors A and B are aligned parallel to each other, as shown in the figure. A light ray is 
incident at an angle of 30° at a point just inside one end of A. The number of times the ray 
undergoes reflections (including the first one) before it emerges out is 
 
  (a) 29    (b) 30   (c) 31    (d) 32 
Q 11.  An object O is just about to strike a perfectly reflecting inclined plane of inclination
 
37°. Its 
velocity is 5 m/s. Find the velocity of its image 
 
 (a) 
ˆˆ
3i 4j ?   (b) 
ˆˆ
4i 3j ?   (c) 
ˆˆ
4.8i 1.4j ?   (d) 
ˆˆ
1.4i 4.8j ?  
Q 12.  An elevator at rest which is at 10th floor of a building is having a plane mirror fixed to its floor. A 
particle is projected with a speed 2 m/s and at 45° with the horizontal as shown in the figure. At 
the very instant of projection, the cable of the elevator breaks and the elevator starts falling freely. 
What will be the separation between the particle and is image 0.5 s after the instant of projection? 
Page 3


For JEE Advanced 
Objective Questions 
  Single Option Correct 
Q 1.  An insect of negligible mass is sitting on a block of mass M, tied with a spring of force constant k. 
The block performs simple harmonic motion with amplitude A in front of a plane mirror placed as 
shown. The maximum speed of insect relative to its image will be 
 
 (a) 
k
A
M
   (b) 
A 3 k
2M
  (c) 
k
A3
M
   (d) 
M
2A
k
 
Q 2.  A plane mirror is falling vertically as shown in the figure. If S is a point source of light, the rate of 
increase of the length AB is 
 
  (a) directly proportional to x   (b) constant but not zero 
  (c) inversely proportional to x  (d) zero 
Q 3.  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 
Q 4.  Two plane mirrors L
1
 and L
2
 are parallel to each other and 3 m apart. A person standing x m from 
the right mirror L
2
 looks into this mirror and sees a series of images. The distance between the first 
and second image is 4 m. Then the value of x is 
 
  (a) 2 m   (b) 1.5 m  (c) 1 m   (d) 2.5 m 
Q 5.  A piece of wire bent into an L shape with upright and horizontal portion of equal lengths 10 cm 
each is placed with the horizontal portion along the axis of the concave mirror towards pole of 
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 portion of the wire is 
  (a) 1 :2   (b) 1:3    (c) 1:1    (d) 2 : 1 
Q 6.  A point object at 15 cm from a concave mirror of radius of curvature 20 cm is made to oscillate 
along the principal axis with amplitude 2 mm. The amplitude of its image will be 
  (a) 2 mm   (b) 4 mm   (c) 8 mm   (d) None of these 
Q 7.  A ray of light falls on a plane mirror. When the mirror is turned, about an axis at right angles to 
the plane of mirror by 20° the angle between the incident ray and new reflected ray is 45°. The 
angle between the incident ray and original reflected ray was therefore 
  (a) 35° or 50°   (b) 25° or 65°  (c) 45° or 5°   (d) None of these 
Q 8.  A person AB of height 170 cm is standing in front of a plane mirror. His eyes are at height 164 
cm. At what distance from P should a hole be made in mirror so that he cannot see his hair 
 
  (a) 167 cm   (b) 161 cm  (c) 163 cm   (d) 165 cm 
Q 9.  Two blocks each of masses m lie on a smooth table. They are attached to two other masses as 
shown in figure. The pulleys and strings are light. An object O is kept at rest on the table. The 
sides AB and CD of the two blocks are made reflecting. The acceleration of two images formed in 
those two reflecting
 
surfaces with respect to each other is 
 
 (a) 
5g
6
   (b) 
5g
3
   (c) 
17g
12
   (d) 
17g
6
 
Q 10. Two plane mirrors A and B are aligned parallel to each other, as shown in the figure. A light ray is 
incident at an angle of 30° at a point just inside one end of A. The number of times the ray 
undergoes reflections (including the first one) before it emerges out is 
 
  (a) 29    (b) 30   (c) 31    (d) 32 
Q 11.  An object O is just about to strike a perfectly reflecting inclined plane of inclination
 
37°. Its 
velocity is 5 m/s. Find the velocity of its image 
 
 (a) 
ˆˆ
3i 4j ?   (b) 
ˆˆ
4i 3j ?   (c) 
ˆˆ
4.8i 1.4j ?   (d) 
ˆˆ
1.4i 4.8j ?  
Q 12.  An elevator at rest which is at 10th floor of a building is having a plane mirror fixed to its floor. A 
particle is projected with a speed 2 m/s and at 45° with the horizontal as shown in the figure. At 
the very instant of projection, the cable of the elevator breaks and the elevator starts falling freely. 
What will be the separation between the particle and is image 0.5 s after the instant of projection? 
 
  (a) 0.5 m   (b) 1m    (c) 2 m   (d) 1.5 m 
Q 13.  A plane mirror is moving with velocity 
ˆ ˆ ˆ
4i 4j 8k ?? . A point object in front of the mirror moves 
with a velocity
ˆ ˆ ˆ
3i 4j 5k ?? . Here 
ˆ
k
 
is along the normal to the plane mirror and facing towards the 
object. The velocity of the image is 
 (a) 
ˆ ˆ ˆ
3i 4j 5k ? ? ?  (b) 
ˆ ˆ ˆ
3i 4j 11k ??  (c) 
ˆ ˆ ˆ
4i 5j 11k ? ? ?  (d) 
ˆ ˆ ˆ
7i 9j 3k ?? 
Q 14.  Point A (0,1 cm) and B (12 cm, 5 cm) are the coordinates of object and image, x-axis is the 
principle axis of the mirror. Then this object image pair is 
  (a) due to a convex mirror of focal length 2.5 cm 
  (b) due to a concave mirror having its pole at (2 cm, 0) 
  (c) due to a concave mirror having its pole at (- 2 cm, 0) 
  (d) Data is insufficient  
Q 15.  Two plane mirrors AB and AC are inclined at an angle ? = 20°. A ray of light starting from point 
P is incident at point Q on the mirror AB, then at R on mirror AC and again on S on AB. Finally 
the ray ST goes parallel to mirror AC. The angle which the ray makes with the normal at point Q 
on mirror AB is 
 
  (a) 20°   (b) 30°   (c) 40°   (d) 60° 
Q 16.  A convex mirror of radius of curvature 20 cm is shown in figure. An object O is placed in front of 
this mirror. Its ray diagram is shown. How many mistakes are there in the ray diagram (AB is 
principal axis) 
 
  (a) 3   (b) 2   (c) 1   (d) 0 
Passage : (Q. No. 17 to 20) 
A plane mirror (M
1
) and a concave mirror (M
2
 ) of focal length 10 cm are arranged as shown in 
figure. An object is kept at origin. Answer the following questions, (consider image formed by 
single reflection in all cases) 
Page 4


For JEE Advanced 
Objective Questions 
  Single Option Correct 
Q 1.  An insect of negligible mass is sitting on a block of mass M, tied with a spring of force constant k. 
The block performs simple harmonic motion with amplitude A in front of a plane mirror placed as 
shown. The maximum speed of insect relative to its image will be 
 
 (a) 
k
A
M
   (b) 
A 3 k
2M
  (c) 
k
A3
M
   (d) 
M
2A
k
 
Q 2.  A plane mirror is falling vertically as shown in the figure. If S is a point source of light, the rate of 
increase of the length AB is 
 
  (a) directly proportional to x   (b) constant but not zero 
  (c) inversely proportional to x  (d) zero 
Q 3.  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 
Q 4.  Two plane mirrors L
1
 and L
2
 are parallel to each other and 3 m apart. A person standing x m from 
the right mirror L
2
 looks into this mirror and sees a series of images. The distance between the first 
and second image is 4 m. Then the value of x is 
 
  (a) 2 m   (b) 1.5 m  (c) 1 m   (d) 2.5 m 
Q 5.  A piece of wire bent into an L shape with upright and horizontal portion of equal lengths 10 cm 
each is placed with the horizontal portion along the axis of the concave mirror towards pole of 
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 portion of the wire is 
  (a) 1 :2   (b) 1:3    (c) 1:1    (d) 2 : 1 
Q 6.  A point object at 15 cm from a concave mirror of radius of curvature 20 cm is made to oscillate 
along the principal axis with amplitude 2 mm. The amplitude of its image will be 
  (a) 2 mm   (b) 4 mm   (c) 8 mm   (d) None of these 
Q 7.  A ray of light falls on a plane mirror. When the mirror is turned, about an axis at right angles to 
the plane of mirror by 20° the angle between the incident ray and new reflected ray is 45°. The 
angle between the incident ray and original reflected ray was therefore 
  (a) 35° or 50°   (b) 25° or 65°  (c) 45° or 5°   (d) None of these 
Q 8.  A person AB of height 170 cm is standing in front of a plane mirror. His eyes are at height 164 
cm. At what distance from P should a hole be made in mirror so that he cannot see his hair 
 
  (a) 167 cm   (b) 161 cm  (c) 163 cm   (d) 165 cm 
Q 9.  Two blocks each of masses m lie on a smooth table. They are attached to two other masses as 
shown in figure. The pulleys and strings are light. An object O is kept at rest on the table. The 
sides AB and CD of the two blocks are made reflecting. The acceleration of two images formed in 
those two reflecting
 
surfaces with respect to each other is 
 
 (a) 
5g
6
   (b) 
5g
3
   (c) 
17g
12
   (d) 
17g
6
 
Q 10. Two plane mirrors A and B are aligned parallel to each other, as shown in the figure. A light ray is 
incident at an angle of 30° at a point just inside one end of A. The number of times the ray 
undergoes reflections (including the first one) before it emerges out is 
 
  (a) 29    (b) 30   (c) 31    (d) 32 
Q 11.  An object O is just about to strike a perfectly reflecting inclined plane of inclination
 
37°. Its 
velocity is 5 m/s. Find the velocity of its image 
 
 (a) 
ˆˆ
3i 4j ?   (b) 
ˆˆ
4i 3j ?   (c) 
ˆˆ
4.8i 1.4j ?   (d) 
ˆˆ
1.4i 4.8j ?  
Q 12.  An elevator at rest which is at 10th floor of a building is having a plane mirror fixed to its floor. A 
particle is projected with a speed 2 m/s and at 45° with the horizontal as shown in the figure. At 
the very instant of projection, the cable of the elevator breaks and the elevator starts falling freely. 
What will be the separation between the particle and is image 0.5 s after the instant of projection? 
 
  (a) 0.5 m   (b) 1m    (c) 2 m   (d) 1.5 m 
Q 13.  A plane mirror is moving with velocity 
ˆ ˆ ˆ
4i 4j 8k ?? . A point object in front of the mirror moves 
with a velocity
ˆ ˆ ˆ
3i 4j 5k ?? . Here 
ˆ
k
 
is along the normal to the plane mirror and facing towards the 
object. The velocity of the image is 
 (a) 
ˆ ˆ ˆ
3i 4j 5k ? ? ?  (b) 
ˆ ˆ ˆ
3i 4j 11k ??  (c) 
ˆ ˆ ˆ
4i 5j 11k ? ? ?  (d) 
ˆ ˆ ˆ
7i 9j 3k ?? 
Q 14.  Point A (0,1 cm) and B (12 cm, 5 cm) are the coordinates of object and image, x-axis is the 
principle axis of the mirror. Then this object image pair is 
  (a) due to a convex mirror of focal length 2.5 cm 
  (b) due to a concave mirror having its pole at (2 cm, 0) 
  (c) due to a concave mirror having its pole at (- 2 cm, 0) 
  (d) Data is insufficient  
Q 15.  Two plane mirrors AB and AC are inclined at an angle ? = 20°. A ray of light starting from point 
P is incident at point Q on the mirror AB, then at R on mirror AC and again on S on AB. Finally 
the ray ST goes parallel to mirror AC. The angle which the ray makes with the normal at point Q 
on mirror AB is 
 
  (a) 20°   (b) 30°   (c) 40°   (d) 60° 
Q 16.  A convex mirror of radius of curvature 20 cm is shown in figure. An object O is placed in front of 
this mirror. Its ray diagram is shown. How many mistakes are there in the ray diagram (AB is 
principal axis) 
 
  (a) 3   (b) 2   (c) 1   (d) 0 
Passage : (Q. No. 17 to 20) 
A plane mirror (M
1
) and a concave mirror (M
2
 ) of focal length 10 cm are arranged as shown in 
figure. An object is kept at origin. Answer the following questions, (consider image formed by 
single reflection in all cases) 
 
Q 17.  The co-ordinates of image formed by plane mirror are 
  (a) (-20cm,0)   (b) (10 cm,-60 cm) (c) (10cm,-10cm)  (d) (10cm, 10cm) 
Q 18.  The co-ordinates of image formed by concave mirror are 
  (a) (10 cm,-40 cm)  (b) (10 cm,-60 cm)  (c) (10 cm, 8 cm)  (d) None of these 
Q 19.  If concave mirror is replaced by convex mirror of same focal length, then coordinates of image  
formed by M
2
 will be 
  (a) (10 cm, 12 cm)  (b) (10 cm, 22 cm)  (c) (10 cm, 8 cm)  (d) None of these 
Q 20.  If concave mirror is replaced by another plane mirror parallel to x-axis then co-ordinates of image  
formed by M
2
 are 
  (a) (40 cm, 20 cm)  (b) (20 cm, 40 cm)  (c) (- 20 cm, 20 cm)  (d) None of these  
Answers 
1.(c) 2.(d) 3.(a) 4.(c) 5.(c) 6.(c) 7.(d) 8.(a) 9.(c) 10.(c) 11.(c) 12.(b) 13.(b) 14.(b) 15.(b) 16.(b)  
17.(c) 18.(d) 19.(d) 20.(d) 
Solutions 
1.  
   V
0 
= V
I
 = ?A 
   
    
2.  
   AB = PB- PA = 2(a + L) - 2a =2L = constant 
3.  
   | ?v | = m
2
| ?v| 
   = (-2)
2
(0.1 cm) 
   = 0.4 cm 
Page 5


For JEE Advanced 
Objective Questions 
  Single Option Correct 
Q 1.  An insect of negligible mass is sitting on a block of mass M, tied with a spring of force constant k. 
The block performs simple harmonic motion with amplitude A in front of a plane mirror placed as 
shown. The maximum speed of insect relative to its image will be 
 
 (a) 
k
A
M
   (b) 
A 3 k
2M
  (c) 
k
A3
M
   (d) 
M
2A
k
 
Q 2.  A plane mirror is falling vertically as shown in the figure. If S is a point source of light, the rate of 
increase of the length AB is 
 
  (a) directly proportional to x   (b) constant but not zero 
  (c) inversely proportional to x  (d) zero 
Q 3.  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 
Q 4.  Two plane mirrors L
1
 and L
2
 are parallel to each other and 3 m apart. A person standing x m from 
the right mirror L
2
 looks into this mirror and sees a series of images. The distance between the first 
and second image is 4 m. Then the value of x is 
 
  (a) 2 m   (b) 1.5 m  (c) 1 m   (d) 2.5 m 
Q 5.  A piece of wire bent into an L shape with upright and horizontal portion of equal lengths 10 cm 
each is placed with the horizontal portion along the axis of the concave mirror towards pole of 
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 portion of the wire is 
  (a) 1 :2   (b) 1:3    (c) 1:1    (d) 2 : 1 
Q 6.  A point object at 15 cm from a concave mirror of radius of curvature 20 cm is made to oscillate 
along the principal axis with amplitude 2 mm. The amplitude of its image will be 
  (a) 2 mm   (b) 4 mm   (c) 8 mm   (d) None of these 
Q 7.  A ray of light falls on a plane mirror. When the mirror is turned, about an axis at right angles to 
the plane of mirror by 20° the angle between the incident ray and new reflected ray is 45°. The 
angle between the incident ray and original reflected ray was therefore 
  (a) 35° or 50°   (b) 25° or 65°  (c) 45° or 5°   (d) None of these 
Q 8.  A person AB of height 170 cm is standing in front of a plane mirror. His eyes are at height 164 
cm. At what distance from P should a hole be made in mirror so that he cannot see his hair 
 
  (a) 167 cm   (b) 161 cm  (c) 163 cm   (d) 165 cm 
Q 9.  Two blocks each of masses m lie on a smooth table. They are attached to two other masses as 
shown in figure. The pulleys and strings are light. An object O is kept at rest on the table. The 
sides AB and CD of the two blocks are made reflecting. The acceleration of two images formed in 
those two reflecting
 
surfaces with respect to each other is 
 
 (a) 
5g
6
   (b) 
5g
3
   (c) 
17g
12
   (d) 
17g
6
 
Q 10. Two plane mirrors A and B are aligned parallel to each other, as shown in the figure. A light ray is 
incident at an angle of 30° at a point just inside one end of A. The number of times the ray 
undergoes reflections (including the first one) before it emerges out is 
 
  (a) 29    (b) 30   (c) 31    (d) 32 
Q 11.  An object O is just about to strike a perfectly reflecting inclined plane of inclination
 
37°. Its 
velocity is 5 m/s. Find the velocity of its image 
 
 (a) 
ˆˆ
3i 4j ?   (b) 
ˆˆ
4i 3j ?   (c) 
ˆˆ
4.8i 1.4j ?   (d) 
ˆˆ
1.4i 4.8j ?  
Q 12.  An elevator at rest which is at 10th floor of a building is having a plane mirror fixed to its floor. A 
particle is projected with a speed 2 m/s and at 45° with the horizontal as shown in the figure. At 
the very instant of projection, the cable of the elevator breaks and the elevator starts falling freely. 
What will be the separation between the particle and is image 0.5 s after the instant of projection? 
 
  (a) 0.5 m   (b) 1m    (c) 2 m   (d) 1.5 m 
Q 13.  A plane mirror is moving with velocity 
ˆ ˆ ˆ
4i 4j 8k ?? . A point object in front of the mirror moves 
with a velocity
ˆ ˆ ˆ
3i 4j 5k ?? . Here 
ˆ
k
 
is along the normal to the plane mirror and facing towards the 
object. The velocity of the image is 
 (a) 
ˆ ˆ ˆ
3i 4j 5k ? ? ?  (b) 
ˆ ˆ ˆ
3i 4j 11k ??  (c) 
ˆ ˆ ˆ
4i 5j 11k ? ? ?  (d) 
ˆ ˆ ˆ
7i 9j 3k ?? 
Q 14.  Point A (0,1 cm) and B (12 cm, 5 cm) are the coordinates of object and image, x-axis is the 
principle axis of the mirror. Then this object image pair is 
  (a) due to a convex mirror of focal length 2.5 cm 
  (b) due to a concave mirror having its pole at (2 cm, 0) 
  (c) due to a concave mirror having its pole at (- 2 cm, 0) 
  (d) Data is insufficient  
Q 15.  Two plane mirrors AB and AC are inclined at an angle ? = 20°. A ray of light starting from point 
P is incident at point Q on the mirror AB, then at R on mirror AC and again on S on AB. Finally 
the ray ST goes parallel to mirror AC. The angle which the ray makes with the normal at point Q 
on mirror AB is 
 
  (a) 20°   (b) 30°   (c) 40°   (d) 60° 
Q 16.  A convex mirror of radius of curvature 20 cm is shown in figure. An object O is placed in front of 
this mirror. Its ray diagram is shown. How many mistakes are there in the ray diagram (AB is 
principal axis) 
 
  (a) 3   (b) 2   (c) 1   (d) 0 
Passage : (Q. No. 17 to 20) 
A plane mirror (M
1
) and a concave mirror (M
2
 ) of focal length 10 cm are arranged as shown in 
figure. An object is kept at origin. Answer the following questions, (consider image formed by 
single reflection in all cases) 
 
Q 17.  The co-ordinates of image formed by plane mirror are 
  (a) (-20cm,0)   (b) (10 cm,-60 cm) (c) (10cm,-10cm)  (d) (10cm, 10cm) 
Q 18.  The co-ordinates of image formed by concave mirror are 
  (a) (10 cm,-40 cm)  (b) (10 cm,-60 cm)  (c) (10 cm, 8 cm)  (d) None of these 
Q 19.  If concave mirror is replaced by convex mirror of same focal length, then coordinates of image  
formed by M
2
 will be 
  (a) (10 cm, 12 cm)  (b) (10 cm, 22 cm)  (c) (10 cm, 8 cm)  (d) None of these 
Q 20.  If concave mirror is replaced by another plane mirror parallel to x-axis then co-ordinates of image  
formed by M
2
 are 
  (a) (40 cm, 20 cm)  (b) (20 cm, 40 cm)  (c) (- 20 cm, 20 cm)  (d) None of these  
Answers 
1.(c) 2.(d) 3.(a) 4.(c) 5.(c) 6.(c) 7.(d) 8.(a) 9.(c) 10.(c) 11.(c) 12.(b) 13.(b) 14.(b) 15.(b) 16.(b)  
17.(c) 18.(d) 19.(d) 20.(d) 
Solutions 
1.  
   V
0 
= V
I
 = ?A 
   
    
2.  
   AB = PB- PA = 2(a + L) - 2a =2L = constant 
3.  
   | ?v | = m
2
| ?v| 
   = (-2)
2
(0.1 cm) 
   = 0.4 cm 
  Object and image travel in opposite directions (along the axis). 
4.  
   I
1
I
2
 = (3 - x) + (3) + x = 4 m  
  Solving we get, x = 1 m 
5.  Image of c with coincide with this. 
   
  For P: 
   
    
  Length of image of PM : 
    
  Length of image of PC : 
    
   
    
   v = - 30 cm 
   
     | ?v| = m
2 
| ?u| 
   = (- 2)
2
 (2 mm) = 8 mm 
7.  Let i is the angle between incident ray and original reflected ray. Then initial angle between them 
will be 180 - 2i. When mirror is rotated by 20° , then reflected ray will rotate by 40° 
   180 - 2i  40° = 45°  
  Solving we get, 
   i = 47.5° or 87.5°