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2th question Consider the arrangement of thin lenses as shown in the figure. An object O is placed at a distance of mR from the system of thin lenses. From the lens system a plane mirror is placed at an unknown distance as shown, for what value of m, image of O and object O will coincide with each other. Consider paraxial rays approximation to be valid.

2th question 
          Consider the arrangement of thin lenses as shown in the figure. An object O is placed at a distance of mR from the system of thin lenses. From the lens system a plane mirror is placed at an unknown distance as shown, for what value of m, image of O and object O will coincide with each other. Consider paraxial rays approximation to be valid. 
 

Question Image
Grade:12

1 Answers

Sahil Yadav
32 Points
one year ago
The first image will be formed from refraction from lens, its position can be determined by lens formulas
 
The lens formulas is given as v1u1=f1...(i)
 
where u=a,f=+f, substituting values in equation (i)
 
v1a1=f1v=afaf
 
The image formed will be left side of lens provide a>f
 
The mirror will form the image at right side of the lens with distance equal to 
 
afaf
 
Now the third image will be formed by lens again for which the coordinate system will be reversed of earlier as the rays are traveling from left to right:
 
u=afaff=+f and v=3a
 
applying lens formulas
 
v1u1=f1...(i)
 
a3afaf=f1...(ii) multiplying and dividing by f 
 
af3fafaf=afa
 
3fa+f=aa=2f
 

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