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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.

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