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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. 
 

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Grade:12

1 Answers

Sahil Yadav
32 Points
3 years 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 v1​−u1​=f1​...(i)
 
where u=−a,f=+f, substituting values in equation (i)
 
v1​−−a1​=f1​⇒v=a−faf​
 
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 
 
a−faf​
 
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=a−faf​, f=+f and v=3a​
 
applying lens formulas
 
v1​−u1​=f1​...(i)
 
a3​−afa−f​=f1​...(ii) multiplying and dividing by f 
 
af3f​−afa−f​=afa​
 
3f−a+f=a⇒a=2f
 

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