What is linear magnification ? Obtain equation of linear magnification for concave mirror.

Explanation

Linear magnification (m) is the ratio of the height of the image (h.) to the height of the object (h).
`thereforem=(h.)/(h)` … (1)

Object of AB = h height is placed on principal axis in front of concave mirror as shown in figure.
Two rays AQ and AP intersect at A. after reflecting from mirror and A. is image of A.
Rays from object AB form image after reflecting from mirror at A.B.. Let A.B. = h..
As per figure, triangles A.B.P and ABP are
therefore `(B.A.)/(BA)=(B.P)/(BP)`
According to sign convention B.A. =- h., BA = h Putting B.P = - v and BP = - u
`(-h)/(h)=(-v)/(-u)`
`therefore (h.)/(h)=-v/u`
`therefore m= -v/u` (`therefore` From equation (1))
For real image, image formed is inverted hence its magnification is negative and for virtual image, image formed is erect hence its magnification is positive.