JEE Main & Advanced Physics Ray Optics Magnification

The ratio of the size of the image to the size of object is called magnification.

(1) Transverse magnification : \[m=\frac{I}{O}=\frac{v}{u}=\frac{f}{f+u}=\frac{f-v}{f}\]  (use sign convention while solving the problem)

(2) Longitudinal magnification : \[m=\frac{I}{O}=\frac{{{v}_{2}}-{{v}_{1}}}{{{u}_{2}}-{{u}_{1}}}\]. For very small object \[m=\frac{dv}{du}={{\left( \frac{v}{u} \right)}^{2}}={{\left( \frac{f}{f+u} \right)}^{2}}={{\left( \frac{f-v}{f} \right)}^{2}}\]

(3) Areal magnification : \[{{m}_{s}}=\frac{{{A}_{i}}}{{{A}_{o}}}={{m}^{2}}={{\left( \frac{f}{f+u} \right)}^{2}}\],   

(\[{{A}_{i}}=\] Area of image,  \[{{A}_{o}}=\]Area of object)

(4) Relation between object and image speed : If an object moves with constant speed \[({{V}_{o}})\]towards a convex lens from infinity to focus, the image will move slower in the beginning and then faster. Also \[{{V}_{i}}={{\left( \frac{f}{f+u} \right)}^{2}}.\,{{V}_{o}}\]