Question

Two converging lenses have focal length $f_{1}$ and $f_{2}$ . The optical axes of the two lenses coincide. This lens system is used to form an image of an object. It is observed that the size of the image does not depend on the distance between the system and object. The distance between lenses is

• A. $\frac{f_{1} f_{2}}{f_{1} + f_{2}}$
• B. $f_{1}+f_{2}$
• C. $\left|f_{1} - f_{2}\right|$
• D. $\frac{\left(f_{1} - f_{2}\right)^{2}}{f_{1}}$

Answer 1

Answer: (B)

For $1^{s t}$ lens, $m_{1}=\frac{f_{1}}{x - f_{1}}$
Where $x_{1}$ is the distance of the object from $1^{s t}$ lens.
For $2^{n d}$ lens, (Let d be the distance between the lenses)
$m_{2}=\frac{x - f_{1}}{\left\{\left(d - f_{1} - f_{2}\right) x - d f_{1} + f_{1} f_{2}\right\}}$
Overall magnification $=m_{1}m_{2}=\frac{f_{1}}{\left\{\left(d - f_{1} - f_{2}\right) x - d f_{1} + f_{1} f_{2}\right\}}$ is independent of x if $d=f_{1}+f_{2}$