JEE Main & Advanced Physics Ray Optics Mirror Formula and Magnification

For a spherical mirror if u = Distance of object from pole, v = distance of image from pole, f = Focal length, R = Radius of curvature, O = Size of object, I = size of image

(1) Mirror formula : \[\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\]

(2) Lateral magnification : When an object is placed perpendicular to the principle axis, then linear magnification is called lateral or transverse magnification.

\[m=\frac{I}{O}=-\frac{v}{u}=\frac{f}{f-u}=\frac{f-v}{f}\]

(* Always use sign convention while solving the problems)

Axial magnification : When object lies along the principle axis then its axial magnification \[m=\frac{I}{O}=\frac{-({{v}_{2}}-{{v}_{1}})}{({{u}_{2}}-{{u}_{1}})}\]

If object is small; \[m=-\frac{dv}{du}={{\left( \frac{v}{u} \right)}^{2}}\] \[={{\left( \frac{f}{f-u} \right)}^{2}}={{\left( \frac{f-v}{f} \right)}^{2}}\]

Areal magnification : If a 2D-object is placed with it's plane perpendicular to principle axis. It's Areal magnification

\[{{m}_{s}}=\frac{\text{Area}\,\text{of}\,\text{image}\,({{A}_{i}})}{\text{Area}\,\text{of}\,\text{object}\,({{A}_{o}})}\]\[\Rightarrow \,\,\,{{m}_{s}}={{m}^{2}}=\frac{{{A}_{i}}}{{{A}_{o}}}\]