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

 Page 1


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Reflection from Plane Surface (Plane Mirror) 
Q 1.  A candle 4.85 cm tall is 39.2 cm to the left of a plane mirror. Where does the mirror form the 
image, and what is the height of this image? 
Q 2.  A plane mirror lies face up, making an angle of 15° with the horizontal. A ray of light shines down 
vertically on the mirror. What is the angle of incidence? What will the angle between the reflected 
ray and the horizontal be? 
Q 3.  Two plane mirrors are placed parallel to each other and 40 cm apart. An object is placed 10 cm 
from one mirror. What is the distance from the object to the image for each of the five images that 
are closest to the object? 
Q 4.  If an object is placed between two parallel mirrors, an infinite number of images result. Suppose 
that the mirrors are a distance 2b apart and the object is put at the midpoint between the mirrors. 
Find the distances of the images from the object. 
Q 5.  Show that a ray of light reflected from a plane mirror rotates through an angle 2 ? when the mirror 
is rotated through an angle ? about its axis perpendicular to both the incident ray and the normal to 
the surface. 
Q 6.  Two plane mirrors each 1.6 m long, are facing each other. The distance between the mirrors is 20 
cm. A light incident on one end of one of the mirrors at an angle of incidence of 30°. How many 
times is the ray reflected before it reaches the other end? 
Q 7.  Two plane mirrors are inclined to each other at an angle ?. A ray of light is reflected first at one 
mirror and then at the other. Find the total deviation of the ray. 
Reflection from Spherical Surface (Convex and Concave Mirror) 
Q 8.  An object 6.0 mm is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a 
radius of curvature of 22.0 cm. 
  (a) Draw principal ray diagram showing formation of the image. 
  (b) Determine the position, size, orientation, and nature (real or virtual) of the image. 
Q 9.  An object 9.0 mm tall is placed 12.0 cm to the left of the vertex of a convex spherical mirror 
whose radius of curvature has a magnitude of 20.0 cm. 
  (a) Draw a principal ray diagram showing formation of the image. 
  (b) Determine the position, size, orientation, and nature (real or virtual) of the image. 
Q 10.  How far should an object be from a concave spherical mirror of radius 36 cm to form a real image 
one-ninth its size? 
Q 11.  An object is 30.0 cm from a spherical mirror, along the central axis. The absolute value of the 
lateral magnification is 
1
2
. The image produced is inverted. What is the focal length of the mirror? 
Q 12.  A concave mirror has a radius of curvature of 24 cm. How far is an object from the mirror if an 
image is formed that is 
  (a) virtual and 3.0 times the size of the object, 
Page 2


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Reflection from Plane Surface (Plane Mirror) 
Q 1.  A candle 4.85 cm tall is 39.2 cm to the left of a plane mirror. Where does the mirror form the 
image, and what is the height of this image? 
Q 2.  A plane mirror lies face up, making an angle of 15° with the horizontal. A ray of light shines down 
vertically on the mirror. What is the angle of incidence? What will the angle between the reflected 
ray and the horizontal be? 
Q 3.  Two plane mirrors are placed parallel to each other and 40 cm apart. An object is placed 10 cm 
from one mirror. What is the distance from the object to the image for each of the five images that 
are closest to the object? 
Q 4.  If an object is placed between two parallel mirrors, an infinite number of images result. Suppose 
that the mirrors are a distance 2b apart and the object is put at the midpoint between the mirrors. 
Find the distances of the images from the object. 
Q 5.  Show that a ray of light reflected from a plane mirror rotates through an angle 2 ? when the mirror 
is rotated through an angle ? about its axis perpendicular to both the incident ray and the normal to 
the surface. 
Q 6.  Two plane mirrors each 1.6 m long, are facing each other. The distance between the mirrors is 20 
cm. A light incident on one end of one of the mirrors at an angle of incidence of 30°. How many 
times is the ray reflected before it reaches the other end? 
Q 7.  Two plane mirrors are inclined to each other at an angle ?. A ray of light is reflected first at one 
mirror and then at the other. Find the total deviation of the ray. 
Reflection from Spherical Surface (Convex and Concave Mirror) 
Q 8.  An object 6.0 mm is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a 
radius of curvature of 22.0 cm. 
  (a) Draw principal ray diagram showing formation of the image. 
  (b) Determine the position, size, orientation, and nature (real or virtual) of the image. 
Q 9.  An object 9.0 mm tall is placed 12.0 cm to the left of the vertex of a convex spherical mirror 
whose radius of curvature has a magnitude of 20.0 cm. 
  (a) Draw a principal ray diagram showing formation of the image. 
  (b) Determine the position, size, orientation, and nature (real or virtual) of the image. 
Q 10.  How far should an object be from a concave spherical mirror of radius 36 cm to form a real image 
one-ninth its size? 
Q 11.  An object is 30.0 cm from a spherical mirror, along the central axis. The absolute value of the 
lateral magnification is 
1
2
. The image produced is inverted. What is the focal length of the mirror? 
Q 12.  A concave mirror has a radius of curvature of 24 cm. How far is an object from the mirror if an 
image is formed that is 
  (a) virtual and 3.0 times the size of the object, 
(b) real and 3.0 times the size of the object and (c) real and one-third the size of the object? 
Q 13.  As the position of an object in front of a concave spherical mirror of 0.25 m focal length is varied, 
the position of the image varies. Plot the image distance as a function of the object distance letting 
the latter change from 0 to + ?. Where is the image real? Where virtual? 
Q 14.  An object is placed 42 cm, in front of a concave mirror of focal length 21 cm. Light from the 
concave mirror is reflected onto a small plane mirror 21 cm in front of the concave mirror. Where 
is the final image? 
Q 15.  Prove that for spherical mirrors the product of the distance of the object and the image to the 
principal focus is always equal to the square of the principal focal length. 
Q 16.  Convex and concave mirrors have the same radii of curvature R. The distance between the mirrors 
is 2R. At what point on the common optical axis of the mirrors should a point source of light A be 
placed for the rays to coverage at the points after being reflected first on the convex and then on 
the concave mirror? 
Solutions 
1.  Image distance from plane mirror = object distance. Lateral magnifications = 1 
2.  
  I ? Incident ray 
  R ? Reflected ray 
  Angle of incidence = 15° 
  Angle between reflected ray and horizontal = 60° 
3.  Image from one mirror will behave like object for other mirror. 
4.  
   O1
1
 = OI
2
 = 2b 
  I
3
 is the image of I
2
 from mirror M
1
 similarly I
4
 is the image of I
1
 from mirror M
2
. 
   OI
3
 = OI
4
 = 4b 
5.  See point number - 3 of important points in reflection from plane mirror. 
6.  
Page 3


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Reflection from Plane Surface (Plane Mirror) 
Q 1.  A candle 4.85 cm tall is 39.2 cm to the left of a plane mirror. Where does the mirror form the 
image, and what is the height of this image? 
Q 2.  A plane mirror lies face up, making an angle of 15° with the horizontal. A ray of light shines down 
vertically on the mirror. What is the angle of incidence? What will the angle between the reflected 
ray and the horizontal be? 
Q 3.  Two plane mirrors are placed parallel to each other and 40 cm apart. An object is placed 10 cm 
from one mirror. What is the distance from the object to the image for each of the five images that 
are closest to the object? 
Q 4.  If an object is placed between two parallel mirrors, an infinite number of images result. Suppose 
that the mirrors are a distance 2b apart and the object is put at the midpoint between the mirrors. 
Find the distances of the images from the object. 
Q 5.  Show that a ray of light reflected from a plane mirror rotates through an angle 2 ? when the mirror 
is rotated through an angle ? about its axis perpendicular to both the incident ray and the normal to 
the surface. 
Q 6.  Two plane mirrors each 1.6 m long, are facing each other. The distance between the mirrors is 20 
cm. A light incident on one end of one of the mirrors at an angle of incidence of 30°. How many 
times is the ray reflected before it reaches the other end? 
Q 7.  Two plane mirrors are inclined to each other at an angle ?. A ray of light is reflected first at one 
mirror and then at the other. Find the total deviation of the ray. 
Reflection from Spherical Surface (Convex and Concave Mirror) 
Q 8.  An object 6.0 mm is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a 
radius of curvature of 22.0 cm. 
  (a) Draw principal ray diagram showing formation of the image. 
  (b) Determine the position, size, orientation, and nature (real or virtual) of the image. 
Q 9.  An object 9.0 mm tall is placed 12.0 cm to the left of the vertex of a convex spherical mirror 
whose radius of curvature has a magnitude of 20.0 cm. 
  (a) Draw a principal ray diagram showing formation of the image. 
  (b) Determine the position, size, orientation, and nature (real or virtual) of the image. 
Q 10.  How far should an object be from a concave spherical mirror of radius 36 cm to form a real image 
one-ninth its size? 
Q 11.  An object is 30.0 cm from a spherical mirror, along the central axis. The absolute value of the 
lateral magnification is 
1
2
. The image produced is inverted. What is the focal length of the mirror? 
Q 12.  A concave mirror has a radius of curvature of 24 cm. How far is an object from the mirror if an 
image is formed that is 
  (a) virtual and 3.0 times the size of the object, 
(b) real and 3.0 times the size of the object and (c) real and one-third the size of the object? 
Q 13.  As the position of an object in front of a concave spherical mirror of 0.25 m focal length is varied, 
the position of the image varies. Plot the image distance as a function of the object distance letting 
the latter change from 0 to + ?. Where is the image real? Where virtual? 
Q 14.  An object is placed 42 cm, in front of a concave mirror of focal length 21 cm. Light from the 
concave mirror is reflected onto a small plane mirror 21 cm in front of the concave mirror. Where 
is the final image? 
Q 15.  Prove that for spherical mirrors the product of the distance of the object and the image to the 
principal focus is always equal to the square of the principal focal length. 
Q 16.  Convex and concave mirrors have the same radii of curvature R. The distance between the mirrors 
is 2R. At what point on the common optical axis of the mirrors should a point source of light A be 
placed for the rays to coverage at the points after being reflected first on the convex and then on 
the concave mirror? 
Solutions 
1.  Image distance from plane mirror = object distance. Lateral magnifications = 1 
2.  
  I ? Incident ray 
  R ? Reflected ray 
  Angle of incidence = 15° 
  Angle between reflected ray and horizontal = 60° 
3.  Image from one mirror will behave like object for other mirror. 
4.  
   O1
1
 = OI
2
 = 2b 
  I
3
 is the image of I
2
 from mirror M
1
 similarly I
4
 is the image of I
1
 from mirror M
2
. 
   OI
3
 = OI
4
 = 4b 
5.  See point number - 3 of important points in reflection from plane mirror. 
6.  
    
  Therefore, actual number of reflections required are 14. 
7.  
   ?
total
 = ?
M
 + ?
N
 
   = (180- 2i) +[180 - 2 ( ? - 0]=360 - 2?
 
8.  (a)  
  (b) Apply, and  
     
9.  (a) 
  (b) Apply, and 
    
10.  f = 
R
2
= -18 cm 
  Let   u = -x cm 
  Then v =
x
9
? cm for real image of 
1
th
9
 
size. 
  Using,  
  we have,  
  Solving we get, x = 180 cm 
11.  Image is inverted. So, it should be real and v should be negative. 
   u = - 30 cm 
Page 4


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Reflection from Plane Surface (Plane Mirror) 
Q 1.  A candle 4.85 cm tall is 39.2 cm to the left of a plane mirror. Where does the mirror form the 
image, and what is the height of this image? 
Q 2.  A plane mirror lies face up, making an angle of 15° with the horizontal. A ray of light shines down 
vertically on the mirror. What is the angle of incidence? What will the angle between the reflected 
ray and the horizontal be? 
Q 3.  Two plane mirrors are placed parallel to each other and 40 cm apart. An object is placed 10 cm 
from one mirror. What is the distance from the object to the image for each of the five images that 
are closest to the object? 
Q 4.  If an object is placed between two parallel mirrors, an infinite number of images result. Suppose 
that the mirrors are a distance 2b apart and the object is put at the midpoint between the mirrors. 
Find the distances of the images from the object. 
Q 5.  Show that a ray of light reflected from a plane mirror rotates through an angle 2 ? when the mirror 
is rotated through an angle ? about its axis perpendicular to both the incident ray and the normal to 
the surface. 
Q 6.  Two plane mirrors each 1.6 m long, are facing each other. The distance between the mirrors is 20 
cm. A light incident on one end of one of the mirrors at an angle of incidence of 30°. How many 
times is the ray reflected before it reaches the other end? 
Q 7.  Two plane mirrors are inclined to each other at an angle ?. A ray of light is reflected first at one 
mirror and then at the other. Find the total deviation of the ray. 
Reflection from Spherical Surface (Convex and Concave Mirror) 
Q 8.  An object 6.0 mm is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a 
radius of curvature of 22.0 cm. 
  (a) Draw principal ray diagram showing formation of the image. 
  (b) Determine the position, size, orientation, and nature (real or virtual) of the image. 
Q 9.  An object 9.0 mm tall is placed 12.0 cm to the left of the vertex of a convex spherical mirror 
whose radius of curvature has a magnitude of 20.0 cm. 
  (a) Draw a principal ray diagram showing formation of the image. 
  (b) Determine the position, size, orientation, and nature (real or virtual) of the image. 
Q 10.  How far should an object be from a concave spherical mirror of radius 36 cm to form a real image 
one-ninth its size? 
Q 11.  An object is 30.0 cm from a spherical mirror, along the central axis. The absolute value of the 
lateral magnification is 
1
2
. The image produced is inverted. What is the focal length of the mirror? 
Q 12.  A concave mirror has a radius of curvature of 24 cm. How far is an object from the mirror if an 
image is formed that is 
  (a) virtual and 3.0 times the size of the object, 
(b) real and 3.0 times the size of the object and (c) real and one-third the size of the object? 
Q 13.  As the position of an object in front of a concave spherical mirror of 0.25 m focal length is varied, 
the position of the image varies. Plot the image distance as a function of the object distance letting 
the latter change from 0 to + ?. Where is the image real? Where virtual? 
Q 14.  An object is placed 42 cm, in front of a concave mirror of focal length 21 cm. Light from the 
concave mirror is reflected onto a small plane mirror 21 cm in front of the concave mirror. Where 
is the final image? 
Q 15.  Prove that for spherical mirrors the product of the distance of the object and the image to the 
principal focus is always equal to the square of the principal focal length. 
Q 16.  Convex and concave mirrors have the same radii of curvature R. The distance between the mirrors 
is 2R. At what point on the common optical axis of the mirrors should a point source of light A be 
placed for the rays to coverage at the points after being reflected first on the convex and then on 
the concave mirror? 
Solutions 
1.  Image distance from plane mirror = object distance. Lateral magnifications = 1 
2.  
  I ? Incident ray 
  R ? Reflected ray 
  Angle of incidence = 15° 
  Angle between reflected ray and horizontal = 60° 
3.  Image from one mirror will behave like object for other mirror. 
4.  
   O1
1
 = OI
2
 = 2b 
  I
3
 is the image of I
2
 from mirror M
1
 similarly I
4
 is the image of I
1
 from mirror M
2
. 
   OI
3
 = OI
4
 = 4b 
5.  See point number - 3 of important points in reflection from plane mirror. 
6.  
    
  Therefore, actual number of reflections required are 14. 
7.  
   ?
total
 = ?
M
 + ?
N
 
   = (180- 2i) +[180 - 2 ( ? - 0]=360 - 2?
 
8.  (a)  
  (b) Apply, and  
     
9.  (a) 
  (b) Apply, and 
    
10.  f = 
R
2
= -18 cm 
  Let   u = -x cm 
  Then v =
x
9
? cm for real image of 
1
th
9
 
size. 
  Using,  
  we have,  
  Solving we get, x = 180 cm 
11.  Image is inverted. So, it should be real and v should be negative. 
   u = - 30 cm 
  Then, v = - 15 cm as magnification is half. 
  Now, applying the equations 
    
   f = - 10 cm 
12.  (a) f = 
R
2
 
= -12 cm 
  Let u = (- x) cm 
  Then, v = (+ 3x) cm as image is virtual and three times magnified. 
  Using the equation 
   * 
    x = 8 cm 
  Similarly, other parts can be solved in the similar manner. For real image v should be negative and 
    |v| = m |u| 
13.  
Object Image 
From O to F or from to O to + 
0.25 m 
From O to - ? 
From F to C or from + 0.25 m to 
+ 0.50 m 
From - ? to C or from + ? to + 
0.50 m 
From C to + ? or from + 0.50 cm 
to + ?  
From C to F or from + 0.50 m to 
+ 0.25 m 
14.  O is placed at centre of curvature of concave mirror (= 42 cm). Therefore, image from this mirror 
I
1
 will coincide with object O. 
    
  Now plane mirror will make its image I
2
 at the same distance from itself. 
15.  
  Using  
Page 5


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Reflection from Plane Surface (Plane Mirror) 
Q 1.  A candle 4.85 cm tall is 39.2 cm to the left of a plane mirror. Where does the mirror form the 
image, and what is the height of this image? 
Q 2.  A plane mirror lies face up, making an angle of 15° with the horizontal. A ray of light shines down 
vertically on the mirror. What is the angle of incidence? What will the angle between the reflected 
ray and the horizontal be? 
Q 3.  Two plane mirrors are placed parallel to each other and 40 cm apart. An object is placed 10 cm 
from one mirror. What is the distance from the object to the image for each of the five images that 
are closest to the object? 
Q 4.  If an object is placed between two parallel mirrors, an infinite number of images result. Suppose 
that the mirrors are a distance 2b apart and the object is put at the midpoint between the mirrors. 
Find the distances of the images from the object. 
Q 5.  Show that a ray of light reflected from a plane mirror rotates through an angle 2 ? when the mirror 
is rotated through an angle ? about its axis perpendicular to both the incident ray and the normal to 
the surface. 
Q 6.  Two plane mirrors each 1.6 m long, are facing each other. The distance between the mirrors is 20 
cm. A light incident on one end of one of the mirrors at an angle of incidence of 30°. How many 
times is the ray reflected before it reaches the other end? 
Q 7.  Two plane mirrors are inclined to each other at an angle ?. A ray of light is reflected first at one 
mirror and then at the other. Find the total deviation of the ray. 
Reflection from Spherical Surface (Convex and Concave Mirror) 
Q 8.  An object 6.0 mm is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a 
radius of curvature of 22.0 cm. 
  (a) Draw principal ray diagram showing formation of the image. 
  (b) Determine the position, size, orientation, and nature (real or virtual) of the image. 
Q 9.  An object 9.0 mm tall is placed 12.0 cm to the left of the vertex of a convex spherical mirror 
whose radius of curvature has a magnitude of 20.0 cm. 
  (a) Draw a principal ray diagram showing formation of the image. 
  (b) Determine the position, size, orientation, and nature (real or virtual) of the image. 
Q 10.  How far should an object be from a concave spherical mirror of radius 36 cm to form a real image 
one-ninth its size? 
Q 11.  An object is 30.0 cm from a spherical mirror, along the central axis. The absolute value of the 
lateral magnification is 
1
2
. The image produced is inverted. What is the focal length of the mirror? 
Q 12.  A concave mirror has a radius of curvature of 24 cm. How far is an object from the mirror if an 
image is formed that is 
  (a) virtual and 3.0 times the size of the object, 
(b) real and 3.0 times the size of the object and (c) real and one-third the size of the object? 
Q 13.  As the position of an object in front of a concave spherical mirror of 0.25 m focal length is varied, 
the position of the image varies. Plot the image distance as a function of the object distance letting 
the latter change from 0 to + ?. Where is the image real? Where virtual? 
Q 14.  An object is placed 42 cm, in front of a concave mirror of focal length 21 cm. Light from the 
concave mirror is reflected onto a small plane mirror 21 cm in front of the concave mirror. Where 
is the final image? 
Q 15.  Prove that for spherical mirrors the product of the distance of the object and the image to the 
principal focus is always equal to the square of the principal focal length. 
Q 16.  Convex and concave mirrors have the same radii of curvature R. The distance between the mirrors 
is 2R. At what point on the common optical axis of the mirrors should a point source of light A be 
placed for the rays to coverage at the points after being reflected first on the convex and then on 
the concave mirror? 
Solutions 
1.  Image distance from plane mirror = object distance. Lateral magnifications = 1 
2.  
  I ? Incident ray 
  R ? Reflected ray 
  Angle of incidence = 15° 
  Angle between reflected ray and horizontal = 60° 
3.  Image from one mirror will behave like object for other mirror. 
4.  
   O1
1
 = OI
2
 = 2b 
  I
3
 is the image of I
2
 from mirror M
1
 similarly I
4
 is the image of I
1
 from mirror M
2
. 
   OI
3
 = OI
4
 = 4b 
5.  See point number - 3 of important points in reflection from plane mirror. 
6.  
    
  Therefore, actual number of reflections required are 14. 
7.  
   ?
total
 = ?
M
 + ?
N
 
   = (180- 2i) +[180 - 2 ( ? - 0]=360 - 2?
 
8.  (a)  
  (b) Apply, and  
     
9.  (a) 
  (b) Apply, and 
    
10.  f = 
R
2
= -18 cm 
  Let   u = -x cm 
  Then v =
x
9
? cm for real image of 
1
th
9
 
size. 
  Using,  
  we have,  
  Solving we get, x = 180 cm 
11.  Image is inverted. So, it should be real and v should be negative. 
   u = - 30 cm 
  Then, v = - 15 cm as magnification is half. 
  Now, applying the equations 
    
   f = - 10 cm 
12.  (a) f = 
R
2
 
= -12 cm 
  Let u = (- x) cm 
  Then, v = (+ 3x) cm as image is virtual and three times magnified. 
  Using the equation 
   * 
    x = 8 cm 
  Similarly, other parts can be solved in the similar manner. For real image v should be negative and 
    |v| = m |u| 
13.  
Object Image 
From O to F or from to O to + 
0.25 m 
From O to - ? 
From F to C or from + 0.25 m to 
+ 0.50 m 
From - ? to C or from + ? to + 
0.50 m 
From C to + ? or from + 0.50 cm 
to + ?  
From C to F or from + 0.50 m to 
+ 0.25 m 
14.  O is placed at centre of curvature of concave mirror (= 42 cm). Therefore, image from this mirror 
I
1
 will coincide with object O. 
    
  Now plane mirror will make its image I
2
 at the same distance from itself. 
15.  
  Using  
   
  Solving this equation we get, 
   xy= f
2 
16.  
  For convex mirror. 
   
   
  Now applying mirror formula for concave mirror we have 
    
  Solving this equation, we can find value of x. 
Objective Questions 
  Single Correct Option 
Q 1.  A plane mirror reflects a beam of light to form a real image. The incident beam should be  
  (a) parallel   (b) convergent  (c) divergent   (d) not possible 
Q 2.  When an object lies at the focus of a concave mirror, then the position of the image formed and its 
magnification are 
  (a) pole and unity     (b) infinity and unity  
(c) infinity and infinity    (d) centre of curvature and unity 
Q 3.  Two plane mirrors are inclined to each other at 90°. A ray of light is incident on one mirror. The 
ray will undergo a total deviation of 
  (a) 180°   (b) 90°   (c) 45°   (d) Data insufficient 
Q 4.  A concave mirror cannot form 
  (a) virtual image of virtual object   (b) virtual image of real object 
  (c) real image of real object    (d) real image of virtual object 
Q 5.  Which of the following is correct graph between u and v for a concave mirror for normal sign 
convention? 
  (a)  (b) (c)  (d)