# JEE Main & Advanced Physics Ray Optics Magnification

Magnification

Category : JEE Main & Advanced

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 ${{V}_{i}}={{\left( \frac{f}{f+u} \right)}^{2}}.\,{{V}_{o}}$

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