# A thin plano- convex lens of focal length f is split into two halves one of halves is shifted along the optical axis. The separation b/w object and image plane is 1.8 m. The magnification of image formed by one of half lenses is 2. Find the focal length of lens and separation b/w the two halves.

$(a)\;0.2\;m \\ (b)\;0.4\;m \\ (c)\;0.6\;m \\ (d)\;0.8 \;m$

This is a modified displacement method problem.
Here distance between screens , $a= 1.8 m$ and distance between two position of lensis d
$\large\frac{a+d}{a-d} =\frac{2}{1}$
Solving we get,
$d= 0.6 \;m$
$\therefore f= \large\frac{a^2-d^2}{4a}$$=0.4 m$
Hence b is the correct answer.

answered Feb 14, 2014 by
edited Jul 23, 2014