Q.Obtain the equation for lateral magnification for a thin lens.

For a thin lens, tracing the undeviated ray through the pole $P$ from an object $OO'$ of height $h_1$ to an image $II'$ of height $h_2$ gives similar triangles $\triangle POO'\sim\triangle PII'$, so $II'/OO'=PI/PO$; applying the sign convention ($h_2=-II'$, $h_1=OO'$, $PI=v$, $PO=-u$) gives the lateral magnification $m=h_2/h_1=v/u$. Combining this with the lens equation gives two equivalent, often more convenient forms: $m=\dfrac{f}{f+u}$ and $m=\dfrac{f-v}{f}$. A negative $m$ signals a real, inverted image; a positive $m$ signals a virtual, erect image. For a converging lens, the image is inverted (real, $m<0$) …