Three convex lens each of focal length 20 cm. are placed co-axially as shown in the figure. Object ‘O’ is placed in front of a lens L₁ at distance of 40 cm and final image by L₃ is framed at 20 cm from it, then distances x and y in the figure are

x = 60 cm, y = any value

The correct answer is Option (2) → x = 60 cm, y = any value

$f_1=f_2=f_3$ = 20 cm

$\frac{1}{f_1}=\frac{1}{v_1}-\frac{1}{u_1}$

$v_1$ = 40 cm

Image by $L_3$ is formed at focus

∴  object for $L_3$ is at $\infty$.

∴  Image formed by $L_2$ is at $\infty ~u_2$ = 20 cm

Object for $L_2$ is placed at 20 cm left form $L_2$ which is 40 cm right $L_1$

∴  x = 40 + 20 = 60 cm

$L_2$ makes image at $\infty$

∴  any distance between $L_2$ and $L_3$ will make object for $L_3$ as $\infty$.

∴  y = any value.