Derive the equation for lateral magnification in spherical mirrors.

Explanation

(i) The lateral or transverse magnification is defined as the ratio of the height of the image to the height of the object. (ii) The height of the object and image are measured perpendicular to the principal axis.
magnification (m) ` = ("height of the image (h')")/("height of the object (h) ")`
` m = (h')/(h)`
Applying proper sign conventions for equation (1),
` (A'B')/(AB) = (PA')/(PA) " " .....(1)`
` A'B' = -h, AB = h, PA' =-v, PA = -u`
`(-h')/(h) = (-v)/(-u)`
On simplifying we get
` m = (h')/(h) = -v/u " " ....(2)`
Using mirror equation , we can further write the magnification as
` m = (h')/( h) = (f -v)/(f) = (f)/(f - u)` ...(3)