The graph shows the variation of the magnification (m) produced by a thin lens with image distance (v). The focal length of the lens is:

$\frac{b}{c}$

The correct answer is Option (4) → $\frac{b}{c}$

Magnification of a lens is,

$m=\frac{v}{u}$

and,

using len's maker formula,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

Multiplying this by 'v'

$\frac{v}{f}=1-m$

and,

$v_1$, image distance from lens = $+a$

$⇒m_1=1-\frac{a}{f}$

$v_2$, image distance from lens = $a+b$

$m_2=1-\frac{a+b}{f}$

$⇒m_2-m_1=c=\frac{b}{f}$

$⇒f=\frac{b}{c}$