In the displacement method, a convex lens is placed in between an object and a screen. If the magnification in the two positions be m1 and m2 and the displacement of the lens between the two positions is X, then the focal length of the lens is :

$x/(m_1 × m_2)$ $x/|m_1 − m_2|$ $x/|m_1 + m_2|$ $x/(m_1 − m_2)^2$

$x/|m_1 − m_2|$

$m_1=\frac{x_1}{x_2}$ & $m_2=\frac{x_2}{x_1}$ $⇒m_1-m_2=\frac{x_1x_2}{x_1+x_2}$ $⇒f=\frac{x}{m_1-m_2}$