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Physics Helpline
L K Satapathy Geometrical Optics 5
Magnification by Lens Mirror System
JEE Question
O
Physics Helpline
L K Satapathy Geometrical Optics 5
Question : Consider a concave mirror and a convex lens ( = 1.5) , each of focal
length 10 cm , separated by a distance of 50 cm in air ( = 1) as shown in the figure.
( ) 2 ( ) 3 ( ) 5 ( ) 7a b c d
Concepts :
O15 cm
50 cm
An object is placed at a distance of 15 cm from the
mirror. The erect image formed by the combination
has a magnification M . When the arrangement is
placed in a medium of refractive index 7/6 , the
magnification becomes M. Then M/ M is
Focal length of a lens of refractive index 
and radii of curvature R1 and R2 is given by 1 2
1 1 1( 1)
f R R

 
   
 
When the lens is placed in a transparent
medium of refractive index  , then 1 2
1 1 11
f R R


  
       
Lens equation1 1 1
v u f
 Mirror equation 1 1 1
v u f
 
Physics Helpline
L K Satapathy Geometrical Optics 5
Answer :
1 1 1 1 1 1 1 1
10 15 15 10 30v f u
        
 
I1
30 cm
50 cm
Reflection by mirror ( in air ) :
1
30 2
15
vm
u
  
10 , 15f cm u cm   
Image I1 is formed 30 cm to the right of the mirror
30v cm  
 Magnification by mirror is
I1 becomes the object for the lens
Physics Helpline
L K Satapathy Geometrical Optics 5
I1
I20 cm 20 cm
Refraction by lens ( in air) :
1 1 1 1 1 1 1 1
10 20 10 20 20v f u
       

2
20 1
20
vm
u
  
1 2 2M m m 
10 , 20f cm u cm  
20v cm 
Image I is formed 20 cm to the right of the lens
 Magnification by lens is
 Magnification by the combination in air is given by
Physics Helpline
L K Satapathy Geometrical Optics 5
1 2
1 2 1 1
' 7f R R
 
   
 
In the medium ( = 7/6) : Reflection by mirror is not affected
1 1 2m m  
  1 2 1 2
1 1 1 1 1 11
2g
f R R R R

   
       
   
3 6 9 21
2 7 7 7
g g
m m
 
 
     
 Magnification by mirror is
Calculation of focal length of lens in the medium :
In air
1 2
1 1 11
'
g
mf R R


  
    
  
In medium
' 1 7 7 7 35' 10
2 2 4 4 2
f
f cm
f
       
We have
Physics Helpline
L K Satapathy Geometrical Optics 5
Correct option = (d)
1 1 1 2 1 8 7 1 ' 140
' ' ' 35 20 140 140
v cm
v f u
        

2
140 7
20
m  
1 2 2 7 14M m m     
14 7
2
[ ]M ns
M
A

 
Refraction by lens ( in medium) :
35 , 20
2
f cm u u cm    
 Magnification by lens in medium is
 Magnification by combination in medium is given by
 The required ratio is
Physics Helpline
L K Satapathy
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Geometrical Optics QA 5

  • 1. Physics Helpline L K Satapathy Geometrical Optics 5 Magnification by Lens Mirror System JEE Question O
  • 2. Physics Helpline L K Satapathy Geometrical Optics 5 Question : Consider a concave mirror and a convex lens ( = 1.5) , each of focal length 10 cm , separated by a distance of 50 cm in air ( = 1) as shown in the figure. ( ) 2 ( ) 3 ( ) 5 ( ) 7a b c d Concepts : O15 cm 50 cm An object is placed at a distance of 15 cm from the mirror. The erect image formed by the combination has a magnification M . When the arrangement is placed in a medium of refractive index 7/6 , the magnification becomes M. Then M/ M is Focal length of a lens of refractive index  and radii of curvature R1 and R2 is given by 1 2 1 1 1( 1) f R R          When the lens is placed in a transparent medium of refractive index  , then 1 2 1 1 11 f R R              Lens equation1 1 1 v u f  Mirror equation 1 1 1 v u f  
  • 3. Physics Helpline L K Satapathy Geometrical Optics 5 Answer : 1 1 1 1 1 1 1 1 10 15 15 10 30v f u            I1 30 cm 50 cm Reflection by mirror ( in air ) : 1 30 2 15 vm u    10 , 15f cm u cm    Image I1 is formed 30 cm to the right of the mirror 30v cm    Magnification by mirror is I1 becomes the object for the lens
  • 4. Physics Helpline L K Satapathy Geometrical Optics 5 I1 I20 cm 20 cm Refraction by lens ( in air) : 1 1 1 1 1 1 1 1 10 20 10 20 20v f u          2 20 1 20 vm u    1 2 2M m m  10 , 20f cm u cm   20v cm  Image I is formed 20 cm to the right of the lens  Magnification by lens is  Magnification by the combination in air is given by
  • 5. Physics Helpline L K Satapathy Geometrical Optics 5 1 2 1 2 1 1 ' 7f R R         In the medium ( = 7/6) : Reflection by mirror is not affected 1 1 2m m     1 2 1 2 1 1 1 1 1 11 2g f R R R R                  3 6 9 21 2 7 7 7 g g m m            Magnification by mirror is Calculation of focal length of lens in the medium : In air 1 2 1 1 11 ' g mf R R              In medium ' 1 7 7 7 35' 10 2 2 4 4 2 f f cm f         We have
  • 6. Physics Helpline L K Satapathy Geometrical Optics 5 Correct option = (d) 1 1 1 2 1 8 7 1 ' 140 ' ' ' 35 20 140 140 v cm v f u           2 140 7 20 m   1 2 2 7 14M m m      14 7 2 [ ]M ns M A    Refraction by lens ( in medium) : 35 , 20 2 f cm u u cm      Magnification by lens in medium is  Magnification by combination in medium is given by  The required ratio is
  • 7. Physics Helpline L K Satapathy For More details: www.physics-helpline.com Subscribe our channel: youtube.com/physics-helpline Follow us on Facebook and Twitter: facebook.com/physics-helpline twitter.com/physics-helpline