Question

show that the linear magnification of an image formed by a curved mirror may be expressed as m=f/(f-u) = (f-v)/f​

Answer 1

For the Linear magnification of the Curved mirror MM'

• Consider a curved mirror MM' with magnification(m) and focal length(f).
• Let u be the object length between object AB and pole,P parallel to the principal axis of the mirror.
• let v be the image length between the image A'B' and pole P parallel to the principal axis.
• The mirror formula is given as:

                                             $\frac{1}{f} =\frac{1}{u} +\frac{1}{v}$

• As the size of the image differs from the size of the object, magnification exists and is expressed as

                                               $m=-\frac{v}{u}$

• from the mirror formula,

                                     $u=\frac{fv}{v-f}\\v=\frac{fu}{u-f}$  

• substituting the above 2 forms in the magnification equation,we get,

                                 $m=\frac{f}{f-u} =\frac{f-v}{f}$