5.2 Longitudinal magnification

When an object lies along the principal axis, then its magnification is known as longitudinal magnification.

It is represented as $m_L$.

From small object, it is given by, $${m_L} = - \frac{{dv}}{{du}}$$ or $${m_L} = - \frac{{dv}}{{du}} = \frac{{{v^2}}}{{{u^2}}}$$ As, $$\begin{equation} \begin{aligned} \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ - \frac{{dv}}{{{v^2}}} - \frac{{du}}{{{u^2}}} = 0 \\ - \frac{{dv}}{{du}} = \frac{{{v^2}}}{{{u^2}}} \\\end{aligned} \end{equation} $$